Statistics Final

P(Z > z0) = 0.9115

-1.35

P(Z < z) = 0.0251

-1.96

P(Z=1.3)

0

P(Z=1.48)

0

P( Z > 5.23)

0.0001

P(Z < -4.5)

0.0001

P(Z < -4.9)

0.0001

The average age for the first marriage for Swedish women is normally distributed with a mean of 32.5 and a standard deviation of 3.2. Find the probability that in a random sample of 16 Swedish women the mean age of marriage is under 28 years. Is this a sample mean or a single data value? What is the distribution?

0.0001, sample mean, ~N(32.5, .8)

Find the probability for the following z score -3.17

0.0008

A multiple choice test has 20 questions with four options for each question. A score of 60% is required to pass. If you randomly guess at each question, what is the probability you pass the Tess assuming there is only one correct answer per problem?

0.001

P(Z < z0) = 0.7422

0.65

P(Z>-3.29)

0.9995

Which of the following would be classified as categorical data?

Hair color

x̄

Statistic

Does the table below represent a correct probability distribution. If not explain why not x=P(x) 0=0.05 1=0.05 2=0.10 5=0.20 10=0.60

Yes, each probability is between one and zero. All probabilities equal one

What is a sample?

a subset of the population

Research has proven that obesity increases your odds of heart disease. This is an example of

causation

What are factors?

independent variables

What is confounding?

when 2 explanatory variables associated in a way their effects on a response variable cannot be distinguished

What is undercoverage?

when some groups in the population are left out of the process of choosing the sample, leaving some bias

What are subjects?

when the experimental units are humans

What is an experimental unit?

who or what we are assigning to a treatment

What is the formula to find the z score of a population?

x - mean / population standard deviation

What is the formula for the confidence interval for a population mean?

x bar - t alpha/2 (s / square root of sample size) < mean < x bar + t alpha/s (s / square root of sample size)

What is the symbol for sample mean?

x̄

What is the symbol for population mean?

μ

What is the symbol for population variance?

σ2

Use the weights of freshmen males in September in the accompanying data set to construct a frequency distribution. Being with a class limit of 50 kg and a class width of 10 kg 77,99,76,93,61,71,63,91,70,69,88,82,65,74,65,69,82,65,55,70,73,74,69,66,63,65,61,73,62,75,72,91

50-59: 1 60-69: 13 70-79: 11 80-89: 3 90-99: 4

The average IQ is 100 with a standard deviation of 15. Find the probability that a randomly selected individual has an IQ of fewer than 80. Is this a sample mean or a single data value? What is the distribution?

0.0918, single data value, ~N(100,15)

P(Z > 1.25)

0.1056

Find P(x) when n=5, p=0.3 and x=3

0.1323

Below is a probability distribution fill in the blank x= P(x) 1=0.02 2=? 3=0.50 4=0.31 5=0.02

0.15

Refer to the sample data for​ pre-employment drug screening shown below. If one of the subjects is randomly​ selected, what is the probability that the test result is a false​ positive? Who would suffer from a false positive​ result? Why? Uses drugs Postive: 44 Negative: 13 Does not use drugs Positive: 13 Negative: 37

0.161. The person tested would suffer because it would look like they use drugs when they don't

Assume that an adult female is randomly selected. Suppose females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. Find the probability of a pulse rate between 61 beats per minute and 68 beats per minute

0.1664

Assume that a procedure yield a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial

0.171

Malaria is responsible for about 40% of all hospitalizations of children under five years old in Malawi according the the President's Malaria Initiative. If fifteen hospitalized children five years and under are randomly selected from Malawian hospitals what is the probability that five of them are hospitalized for malaria?

0.186

Assume that a randomly selected subject is given a bone density test. These test scores are normally distributed with a mean of 0 and a standard deviation of 1. find the probability of a bone density test score greater than 0.76

0.2236

Assume that an adult is randomly selected the probability that they don't require vision correction is 24%. If 9 adults are randomly selected, find the probability that exactly 3 of them don't require vision correction

0.224

The table below displays results from experiments with polygraph instruments. Find P(Subject lied | negative test result). Compare this result with the probability of selecting a subject with a negative test result, given that the subject lied. Are P(subject lied | negative test result) and P(negative test result | subject lied) equal? Positive: Did not lie: 14 Lied: 34 Negative Did not lie: 45 Lied: 10

0.227, 0.182 and these values are not equal

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability p of success on a single trial

0.264

P(-1.24 < Z < 0.05)

0.3726

If a coin is tossed three times, what is the probability of tossing two heads?

0.375

Suppose 5% of Americans own yellow cars. If we randomly elect 10 Americans, what is the probability that at least one of them owns a yellow car? Round to 4 decimal places?

0.4013

A food safety guideline is that mercury in fish should be bellow 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 90% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in the sushi? 0.51, 0.80, 0.10, 0.87, 1.30, 0.59, 0.92

0.451 < u < 1.004. Yes, because it is possible that the mean is greater than 1 ppm. Also, at least one of the sample values exceeds 1 ppm, so at least one of the fish have too much mercury

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 58 tablets then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted or will many be rejected?

0.477. Many would be rejected

In a week before and the week after a holiday, there were 10,000 total deaths, and 4958 of them occurred in the week before the holiday. A) Construct a 90% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday

0.488 < p < 0.504. No, because the proportion could easily equal 0.5. The interval is not less than 0.5 the week before the holiday

In a certain region, the probability of a baby being born a girl is 0.483 instead of 0.5. Let A denote the event of getting a girl when a baby is born. wHat is the value of P(A)

0.517

Assume that random guesses are made for 13 multiple choice questions on a medical admissions test so that there are n=13 trials, each with a probability of success (correct) given by p=0.25. Find the probability that the number x of correct answers is less than 4

0.584

In a certain country, the true probability of a baby being a girl is 0.475. Among the next six randomly selected births in that country, what is the probability that at least one of them is a boy

0.989

Refer to the accompanying technology display. The probabilities in the display were obtained using the values of n=5 and p=0.774. In a clinical test of a drug, 77.4% of the subjects treated with 10 mg of the drug experienced headaches. In each case, assume that 5 subjects are randomly selected and treated with 10 mg of the drug. Find the probability that more than one subject experiences headaches. Is it reasonable to expect that more than one subject will experience headaches? 0=0.0006 1=0.0101 2=0.0692 3=0.2368 4=0.4055 5=0.2778

0.9893. yes, because the event that the number of subjects that experience headaches is less than or equal to one is unlikely.

Heights of adult male giraffes are normally distributed with a mean of 138 inches and a standard deviation of 4 inches. Suppose a random sample of 25 adult male giraffes is selected, what is the probability that the average height of this sample is 130 and 140 inches. Is this a sample mean or a single data value? What is the distribution?

0.9937, sample mean, ~N(138,.8)

Weights of adult human lungs are normally distributed with a mean of 5 pounds and a standard deviation of 0.2 pounds. Find the probability that a randomly selected set of human lungs weights more than 4.5 pounds. Is this a sample mean or a single data value? What is the distribution?

0.9938, single data value and ~N(5,.2)

P(Z < 5.34)

0.9999

Suppose the probability of a student not owning a car is 0.12. If 5 students are selected what is the probability that at least of them owns a car?

0.99998

What are the basic probability rules?

1. Any probability is between 0 and 1 2. The sum of all possible outcomes is 1

What is the empirical rule for data with a bell shaped distribution?

1. Approximately 68% of the observations fall within the standard deviation of the mean 2. Approximately 95% of the observations fall within 2(standard deviation) of the mean 3. Approximately 99.7% of the observation fall within 3(standard deviation) of mean

How do you obtain low variability?

1. Increase sample size 2. Use a sampling design that best reflects the population

How do you obtain low bias?

1. Make sure all members of the population have a nonzero chance of being selected 2. Use a probability based sampling design 3. Reduce the chance of nonresponse and response bias from entering study

What are the rules for normal probability calculations?

1. Remember that your table gives you the probability P(Z<z) or P(Z ≤ z) 2. P(Z>z)=1-P(Z<z) 3. P(a<Z<b) = P(Z<b) - P(Z<a) 4. P(Z=z)=0 5. P(Z<z) = P(Z ≤ z)

What are the properties of normal curves?

1. Symmetric, unimodal, and bell shaped 2. Both mean and median are always in the center of the curve 3. the standard deviation controls the spread (where the curve changes directions) 4. Changing the mean without changing the standard deviation moves the curve along the horizontal axis without change the spread 5. The curve is completely determined by mean and standard deviation 6. The distribution is abbreviated N(mean, standard deviation) 7. Probabilities are the area under the curve between the points of interest

What are the requirements for probability distribution?

1. The sum of all probabilities must be 1 2. Each probability value must be greater than or equal to 0 and less than or equal to 1

What are assumptions?

1. The units (subjects) are selecting using simple random sample. if other sampling designs are used, slightly different formulas will be used 2. the distribution of the data needs to be approximately normally distributed for the T-confidence interval. The smaller the sample size, the more normal the data needs to be. Typically, if the sample size is 30 or more, it is fine to use the T-confidence interval even when the distribution is not normally distributed

What are the requirements for a binomial probability distribution?

1. There are a fixed number of trials 2. The trials are independent 3. All outcomes must be classified into two categories (typically success and failure) 4. The probability of success must remain the same in all trials

What are the assumptions?

1. Use the interval when both the number of successes and the number of failures are at least five 2. the units (subjects) are collected using a simple random sample. If any other sampling designs are used, slightly different formulas are used

P(Z > z) = 0.1022

1.27

A student took the ACT and scored a 26. Calculate their z score and interpret it. Assume that the average ACT score at the time the student took the test was 20.1 with a standard deviation of 4.6

1.28 or 84%

P(Z < z0) = 0.9115

1.35

Find the indicated z score z0=0.9251

1.44

Which of the following values cannot be probabilities? 0.06, -0.46, 1, square root of 2, 3/5, 5/3, 1.48 and 0

1.46, 5/3, -0.46, square root of 2

Find the interquartile range for percent body fat for the 20 individuals below: 5.1, 6.9, 7.5, 8.5, 10.9, 12.0, 12.6, 12.8, 19.0, 20.5, 20.5, 20.5, 20.6, 20.8, 21.7, 21.7, 22.4, 24.6, 27.8, 40.1

10.52

14 different second year medical students at a hospital measured the blood pressure of the same person. The systolic (mm Hg) are listed below. Use the given data to identify the 5 number summary. 125, 134, 135, 136, 120, 125, 124, 130, 127, 122, 135, 140, 138, 150

120.00, 125.0000, 132.0000, 136.0000, 150.00

Use the data on the following table, which summarized blood groups and Rh types for randomly selected subjects. Assume subjects are randomly selected from those included in the table O blood type Rh+: 55 Rh-: 13 A blood type Rh+: 35 Rh-: 11 B blood type Rh+: 8 Rh-: 5 AB blood type Rh+: 11 Rh-: 1 If one person is selected, find the probability of getting someone who is group A or type Rh+. Are these events disjoint

120/139. The event of selecting someone who is group A and the even of selecting someone who is type Rh+ are not disjoint because there is overlap

The average life expectancy of a beagle is 13.3 years with standard deviation of 0.4 years. Assuming that the life expectancies follow a normal distribution. What is the 25th percentile for life expectancies of beagles?

13.032 years

The average life expectancy of a beagle is 13.3 years with standard deviation of 0.4 years. Assuming that the life expectancies follow a normal distribution. The beagles with the highest 25% of life expectancies live how many years?

13.568 years

In a study of acid rain, a random sample of 100 trees from a particular forest was examined. 40% of the selected trees showed some signs of damage. Which of the following statements is true?

40% is the value of the statistic

Find the median of the 9 life expectancies below: 70.5, 65, 70, 51.5, 57.5, 61, 78.5, 72.7, 72

70

What are treatments?

Specific experimental condition applied to the units

What are the factors?

Specific experimental variables being tested

What are factor levels?

Specific level of a factor

What are factor levels?

Specific levels of the factors in the experiment

A study is conducted to find out how many students receive flu shots. It is known prior to the study that females are more likely to get flu shots. The population is divided into two groups: males and females. A random sample of 100 students is taken from each group. What type of sampling design is this?

Stratified random sample

To determine the average gas mileage for cars produced in 2019, 20 small, 20 large and 20 midsized cars were randomly selected. This is an example of a

Stratified random sample

What is an experiment?

Study where treatments are applied to units

What is mean?

Sum of the measurements divided by the total number of measurements

What is the symbol for population standard deviation?

σ

Assume a subject is randomly selected and given a bone density test. Find P12, the 12th percentile. This is the bone density score separating the bottom 12% from the top 88%

-1.18

When do you use a pie graph?

-Categorical data -when wanting to show percentage

When do you use a histogram?

-Quantitative data -when wanting to see overall shape of distribution

A clinical trials tests a method designed to increase the probability of conceiving a girl. In the study 520 babies were born, and 286 of them were girls. Use the sample to construct a 99% condense interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

0.494 < p < 0.606. No, the proportion of girls is not significantly different from 0.5

Find the 75th percentile

0.67

P(Z < 1.04)

0.8508

Find the probability for the following z score z=1.43

0.9236

P(Z ≤ 1.48)

0.9306

P(Z<1.48)

0.9306

The Center for Disease Control and Prevention (CDC) estimated that, last year in the US, 20% of the population got the flu. What sample size would be needed to get a 2 percentage point margine of error on a 90% confidence interval for the population proportion of Americans who get the flu this year?

1083

Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. P(x<x)=0.75

110.1

Find the interquartile range for the 9 life expectancies below: 70.5, 65, 70, 51.5, 57.5, 61, 78.5, 72.7, 72

13.1

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.9 in. and a standard deviation of 1.1 in. Find P99. That is, find the hip breadth for men that separates the smallest 99% from the largest 1%.

17.5

Find the standard deviation for the following data using hand calculations: 6, 7, 9, 11, 12

2.5

Find the median for percent body fat for the 20 individuals listed below: 5.1, 6.9, 7.5, 8.5, 10.9, 12.0, 12.6, 12.8, 19.0, 20.5, 20.5, 20.5, 20.6, 20.8, 21.7, 21.7, 22.4, 24.6, 27.8, 40.1

20.5

The length of pregnancies are normally distributed with mean 268 days and standard deviation of 15 days. If the duration of the pregnancy is in the lowest 3%, the baby is considered premature. Find the cut off for the length of a pregnancy for babies that are considered premature.

2398

the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. A) The probability that a pregnancy will last 309 days or longer is B) Babies who are born on or before ___ days are considered premature. (If the length of a pregnancy is in the lowest 4%, then the baby is considered premature.)

242

Find the five number summary for percent body fat for the 20 individuals listed below: 5.1, 6.9, 7.5, 8.5, 10.9, 12.0, 12.6, 12.8, 19.0, 20.5, 20.5, 20.5, 20.6, 20.8, 21.7, 21.7, 22.4, 24.6, 27.8, 40.1

5.1, 11.45, 20.5, 21.7, 40.1

An athletic association wants to sponsor a footrace. The average time it takes to run the course is 58.6 minutes, with standard deviation of 4.3 minutes. If the association decides to include only the top 20% of the racers, what should the cutoff time be in the tryout run? Assume the variable is normally distributed

54.988 minutes

Suppose you want to estimate the proportion of students who receive the flu shot each year to within 0.03 with 95% confidence. Assume that a previous study found that typically only 15% of college students receive flu shots. How many students will you need to survey?

545 students

Find the sample size needed to estimate the percentage of Oklahoma residents who are left handed. Use a margin of error of four percentage points, and use a confidence level of 95% assume p hat and q hat are unknown

601

Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. P(x>x0)=0.97

71.8

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 20. Find Upper P15 which is the IQ score separating the bottom 15% from the top 85​%.

79.20

Find the mean of the following numbers: 6,7,9,11,12

9

A data set includes 109 body temperatures of healthy adult humans having a mean of 98.2 degrees F and a standard deviation of 0.62 degrees F. Construct a 99% confident interval estimate of the mean body temperature of all healthy human. What does the sample suggest about the use of 98.6 degrees F as the mean body temperature?

98.356. This suggests that the mean body temperature is lower than 98.6 degrees F

To determine the consequences of diet and exercise on blood pressure, 100 volunteers were recruited for a study. They were randomly divided into 4 groups, group 1 was no exercise and a regular diet, group 2 was no exercise and a low sugar diet, group 3 was exercise for 20 minutes and a low regular diet, group 4 was exercise for 20 minutes and a low sugar diet. This is an example of a

A completely randomized design

What is a nonzero axis?

A misleading tactic because one or both of the axes begin at some value other than zero and exaggerate differences

What is the standard normal distribution?

A normal distribution with a mean of 0 and a standard deviation of 1.

What is a statistic?

A number that describes a sample. Can vary from sample to sample

How do a parameter and a statistic differ?

A parameter is a numerical measurement of a population a statistic is a numerical measurement of a sample

What is a histogram?

A picture of a frequency distribution, the horizontal scale represents classes of data values and the vertical scale represents frequencies

What is a voluntary response sample?

A sample in which the subjects themselves decide whether to be included in the study

What is depicting one dimensional data with three dimensional boxes?

A way of representing data that can exaggerate differences

Suppose we have a group of 3 males and 4 females A) What is the probability that we randomly select 2 males? Assume with replacement B) What is the probability that we randomly select 2 males? Assume without replacement?

A) 0.1837 B) 0.1429

What are treatments?

All combinations of factors at different levels.

What is a simple event?

An event with only one outcome

Which word is associated with multiplication when computing possibilities?

And

What is an event?

Any collection of outcomes of a procedure

What is a compound event?

Any even combining two or more simple events

What are the requirements to establish causation from an observational study if an experiment is not possible or realistic?

Association is strong, association is constant over many studies, the alleged cause exceeds the effect in time and the alleged cause is plausible

What is a confidence interval?

Calculated from the sample data and it provides an interval estimate of the population parameter

What is the 1.5 x IQR rule for outliers?

Call an observation a suspected outlier if it falls more than 1.5 X IQR above the third quartile or below the first quartile

What is a bar graph?

Categories are listed on the x-axis and the height of the bars represent the frequency for each category

What are variables?

Characteristic of the units/individuals

Identity the class width, and class boundaries for given frequency distributino Height (in) and frequency 58.0-59.9: 4 60.0-61.9: 25 62.0-63.9: 9 64.0-65.9: 1 66.0-67.9: 0 68.0-69.9: 0 70.0-71.9: 0 72.0-73.9: 0 74.0-75.9: 0 76.0-77.9: 1

Class width: 2 Class midpoints: 58.95, 60.95, 62.95, 64.95, 66.95, 68.95, 70.95, 72.95, 74.95, 76.95

Identify the class width and midpoints for the given frequency distribution: Daily Temperature and frequency 45-48: 1 49-52: 3 53-56: 5 57-60: 11 61-64: 7 65-68: 7 69-72: 1

Class width: 4 Class midpoints: 46.5, 50.5, 54.5, 58.5, 62.5, 66.5

Identify the class width and class midpoints for the given frequency distribution White blood cell count for males and frequency 4.0-7.9: 8 8.0-11.9: 15 12.0-15.9: 11 16.0-19.9: 5 20.0-23.9: 1

Class width: 4 Class midpoints: 5.95, 9.95, 13.95, 17.95, 21.95

How do you create a random number generator using your calculator?

Click prb button, go to RAND and select randint( and type in range desired

What is quantitative data?

Consists of numbers representing counts or measurements

What is a voluntary response sample?

Consists of people who choose themselves by responding to a general appeal

What is categorical data?

Consists of placing units or individuals into groups

The amount of times it takes to complete an example problem. Discrete or continuous random variable?

Continuous

The weight of a feather. Discrete or continuous random variable?

Continuous

What is probability distribution?

Description that gives the probability for each value of the random variable. Often expressed in the format of a graph, table or formula

What is standard deviation?

Differences between each value and the mean squared

The amount of paper used by students each semester. Discrete or random variable?

Discrete

The cost of conducting a genetics experiment. Discrete or continuous random variable?

Discrete

What is the interquartile range (IQR)

Distance between first and third quartiles

What is a population?

Entire group of units or individuals about which we desire information

To determine whether diet will increase the life span of poodles, 20 poodles are put on a special diet and 20 are put on a generic diet and their life span is recorded and compared between groups. Observational study or experiment?

Experiment

What are subjects?

Experimental units that are human beings

When do you use IQR?

Extremely skewed or contain outliers

When do you use median?

Extremely skewed or contains outliers

What is the variance equation?

For every value, find the difference between it, the mean, and square it. Divide the "sum of the squares" by sample size minus one

What is a pie chart?

Graph depicting quantitative data as slices of a pie

What is a modified box plot?

Graph of the five number summary with suspected outliers plotted individually -Central box spans quartiles -A line in the box marks median -Observations more than 1.5 X IQR outside the central box are plotted individually as possible outliers -Lines extend from box out to the smallest and largest observations that are not suspected outliers

What is a discrete random variable?

If the random variable can take on any one of a number of values that can be counted, and if those values are always whole numbers (such as number of items sold), the random variable is called a discrete random variable

Which of the following is always true?

In a symmetric and bell-shaped distribution, the mean, median, and mode are the same

To decrease the variability in our statistic, which of the following would work best?

Increase sample size

What is an experimental unit?

Individual or units on which the experiment is done

Which of the following is not true concerning a parameter?

It has variability associated with it

When randomly selecting an​ adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. Upper P left parenthesis Upper B or Upper B overbar right parenthesis = 1

It is certain that the selected adult has type B blood or does not have type B blood

What is a frequency distribution?

Lists data values along with their corresponding frequencies

The x-axis of the histogram shows

Lower class limits

What does disjoint mean?

Mutually Exclusive (cannot occur at the same time)

Randomly selecting a nurse and randomly selecting a male. Disjoint or no?

No

Ten unique students in a statistics class of 35 students are randomly chosen and whether or not they smoke is recorded. Is this a binomial probability distribution?

No, because the class size is too small, so the probability of success will not remain consistent from one trial to the next

Rolling a dice and recording the number showing on the upward facing side. Is this a binomial probability distribution?

No, because there are more than two outcomes

What is a lurking variable?

Not accounted for in the study but affects the value of the response variable

What is an explanatory variable?

One that causes change in the response variable

What is considered an unusual value?

One that has a probability that is less than 0.05 or one that is two standard deviation from the mean

What is a density curve?

One that is always above the horizontal axis and has an area of exactly 1 underneath it

What is the formula for the multiplication rule for independent events?

P (A and B) = P(A)P(B)

What is the addition rule?

P(A or B) = P(A) + P(B) P(A or B) = P(A) + P(B) - P(A and B)

What is the formula for multiplication rule for dependent events?

P(B | A) = P(A and B) / P(A)

μ

Parameter

Which of the following groups has terms that can be used interchangeably with the other?

Percentage, probability and proportion

What is a categorical variable?

Places individual into one of several groups or categories. Typically described with either a bar or pie graph

What is a stratified random sample?

Population is divided into groups of similar individuals and a simple random sample is chosen separately from each group. Works well when the units are not homogenous with respect to the variable of interest

What is stratified random sampling?

Population is split into CATEGORIES and then pure random selection of certain number of people within each category

What does P stand for?

Probability

What does P(A) stand for?

Probability of event A occurring

When randomly selecting adults, let M denote the even of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)?

Probability of getting a make, given that someone with blue yees has been selected. P(B|M) is not the same because it is the probability of getting someone with blue eyes, given that a male has been selected

What is the bounds for non outliers equation

Q1-1.5 X IQR and Q3 + 1.5 X IQR

How does sampling error occur?

Random chance

A researcher is interested in investigating the relationship between sugar consumption and weight gain for high school students. Because he thought the effect may be different for males and females, he randomly assigned five males and five females to group A and fives males and five females to group B. Group A was put on a low sugar diet and group B was put on a diet that allowed sugar. After eight weeks, the change in weight was recorded for each of the students. What type of experimental design is this?

Randomized block design

What is a unit?

Represents an individual person, animal or object upon which the response variable or variable of interest is measured

What is response bias?

Respondent lies or a recording error occurs

When trying to estimate the number of gloves that nurses go through in a 12 hour shift, some of the nurses in the sample incorrectly recorded the number of gloves they used. This caused what kind of bias?

Response

Which of the following corresponds to the case when every sample size n has the same chance of being chosen?

Sample random sample

What is a control group?

Set of experimental units that receive no active treatment. If said units are subjects, then they usually receive a placebo

To determine the average proportion of bottles in a six pack of vitamin water that had the seals broken, 24 six packs of vitamin water were selected and the proportion of bottles in each of the packs that had the seal broken was recoded. This is an example of a

Simple random sample

To gather data on a 1200 acre pine forest in Colorado, the U.S. Forest Service laid a grid dividing the land into one acre plots. A random sample of 100 pots was selected and information was gathered on these 100 plots. What type of sampling design is this?

Simple random sample

If the scenario describes an observational study

Simple random sample and stratified random sample

What do A,B and C stand for?

Specific events

A random sample of 100 women showed that 5.6% of them smoke. Parameter or statistic?

Statistic

Determine whether the underlined number is a statistic or parameter. A sample of employees is selected and it is found that 25% own a television.

Statistic because the value is a numerical measurement describing a characteristic of a sample

When do you use mean?

Symmetric distribution with no extreme outliers

When do you use standard deviation?

Symmetric distribution with no extreme outliers

To determine how the weight of a vehicle impacts the gas mileage, Ann randomly select 10 compact cars, 10 midsized cars, 10 SUVS, 10 vans and 10 trucks and records the weight in pounds and the gas mileage in miles per gallon for each of the vehicles. What is the sample?

The 50 randomly selected vehicles

Which of the following statements is incorrect about trying to establish causation between two variables?

The association between the 2 variables can be determined through one observational study

What is probability?

The chance of an event occuring

What is the class width?

The difference between two consecutive class limits

Identify whether the given value is a statistic or parameter. A research team has received a collection of brain those deceased in a natural disaster which had been donated for research. It was found that the average (mean) for the volume of the brain they had received was 1059.6 cm^3. They came to this conclusion after measuring the brains they had received

The given value is a statistic because it describes a characteristic of a sample

What is a control group?

The group that does not receive the experimental treatment in an experiment.

What is an upper class limit?

The largest number contained in each class

Assume that 1100 births are randomly selected and 1064 of the births are girls. Use subjective judgement to describe the number of girls as significantly high, significantly low or neither

The number of girls is significantly high

What do histograms show you?

The overall pattern of the data and if any outliers or gaps exist, the overall shape of distribution

What is conditional probability?

The probability of even B occurring after it is assumed that even A has already occurred

What is an outcome?

The result of a single trials of an experiment

What is a lower class limit?

The smallest number contained in each class

What is a completely randomized design?

The treatments are randomly assigned to the experimental units without restriction. All experimental units are allocated at random Among the treatments. It is a lot like simple random sample

Which of the following is NOT a census?

To calculate the proportion of students at their school who use eyes glasses or contacts, the principal asks all students in the 9th grade English class whether they wear eye glasses or contacts

What is the purpose of statistics?

To gain understanding by collecting, organizing and interpreting data

Due to 2 outliers, the median and IQR are the best measures of center and spread because these measures are resistant to outliers. The outliers would have a big impact on the mean and standard deviation as they are nonresistant measures.

True

It would be unusual for 1/20 people to have diabetes because it falls outside the range of 2-2(1.34), 2+2(1.34)

True

What are independent events?

Two events whose occurrence does not affect each other

What is a random variable?

Value is a numerical outcome of a random phenomenon

What is a lurking variable?

Variable that is not among the explanatory or response variables in a study yet may influence the interpretation of relationships among those variables

What is the response variable?

Variable that measures the outcome of a study

What is sampling variability?

Variation associated with the value of the statistic that is generated by repeatedly selecting samples of the same size, using the same probability sampling design from the population

Anne Landers asked people to send her a response to the following question. "Do you have children? If so, would you still have children knowing what you know now?" What type of sampling design is this?

Voluntary response sample

To determine what his classes felt about the last assignment, an instructor emailed his students asking for feedback. This is an example of a

Voluntary response sample

Which of the following would be the correct interpretation of a 99% confidence interval such as 4.1 < u < 5.6?

We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of the mean

What is an observational study?

We let nature do its thing and observe the response. Units are not manipulated in any way, environmental factors are not controlled or manipulated. Possible lurking variables could exist and multiple studies have to be conducted to draw conclusions regarding causality

What is the distribution of a variable?

What values a variable takes and how often it takes those values

What is causation?

When one variable causes a change in the other variable

Randomly selecting a fly that has red eyes and randomly selecting a fly with sepia (dark brown eyes). Disjoint or no?

Yes

What is causation?

a casual relationship exists if a change in one variable results in a change in the other

Is midrange a measure of center of spread?

center

What is simple random sampling?

every member of the population has an equal probability of being selected for the sample

What is a continuous random variable?

infinitely many values

What is the midrange equation?

min + max /2

To estimate the average height of her 5th grade students, a teacher randomly selects 10 students and measures their height. This is an example of an

observational study

What is an observational study?

observes individuals and measures variables of interest but does not attempt to influence the responses

Is IQR a measure of center of spread?

spread

What is the margin of error formula?

t alpha/2 (s / square root of sample size)

What is bimodal?

two peaks

Class width is found by

subtracting a lower class limit from the next consecutive lower class limit

What is a randomized block design?

the random assignment of experimental units to treatments is carried out separately within each block

What is a sample space?

the set of all possible outcomes

Find the area of the shaded region. The graph to the right depicts the IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 On the left side: 80

0.0918

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean=0 and a standard deviation=1. Find probability that a given score is less than -1.37

0.9664

What is the formula to find the z score of a sample?

(x - x bar) / s

What is the formula for z for the central limit theorem?

(x-bar - mean) / (standard deviation / square root of sample size)

What is the formula for determining sample size?

(z alpha/2 / E)^2 p̂qˆ

Find indicated z score. The graph depicts the standard normal distribution of bone density scores with mean=0 and standard deviation=1. On the right side=0.7611

-0.71

Find the indicated z score z0=0.1894

-0.88

In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in processed tablet form. Cholesterol levels were measured before and after the treatment. The change (before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.4 and a standard deviation of 19.3. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL levels?

-1.33 < u < 8.13 mg/dL. The confidence interval limit contains 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels

Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard deviation of 1.00. Assume 3% of thermometers are rejected because they have readings that are too high and another 3% are rejected because they have readings that are too low. Find 2 readings that are cutoff values separating the rejected thermometers from the others

-1.88 and 1.80

Assume a subject is randomly chosen and given a bone density test. Find the probability of the test score being between -2.04 and 2.04

0.9793

In a test of effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.6 and a standard deviation of 17.4. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?

-3.22 < u < 10.42. The confidence level contains 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels

When do you use a modified box plot or side-by-side box plot?

-Quantitative data -when wanting to show upper and lower bounds of middle 50% of data -when wanting to show 5 number summary and test for outliers -when wanting to compare 2 or more groups

When do you use a bar graph?

-When you want frequency

Assume that random guesses are made for 8 multiple choice questions on a test with 2 choices for each question, so that there are n=8 trials, each with a probability of success (correct) given by p=0.50. Find the probability of no correct answers

.004

The table to the right shows the results from a test for a disease among a group of patients. Find the probability of selecting a subject with a positive test realist, given that the subject doesn't have the disease. Why is this case problematic for test subjects? Disease Positive: 357 Negative: 15 No disease Positive: 6 Negative: 1141

0.00523. It is problematic because a false positive could cause unnecessary stress, medication and testing

The average life expectancy of a beagle is 13.3 years with standard deviation of 0.4 years. Assuming a simple random sample of 25 beagles is selected, what is the probability that their average life span is less than 13.1 years?

0.0062

The probability of a randomly selected adult in one country being infected with a certain virus is 0.001. In tests for the virus, blood samples from 30 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus

0.0296

P(1.65 < Z < 2.31)

0.0391

The average life expectancy of a beagle is 13.3 years with a standard deviation of 0.4 years. Assuming that the life expectancies follow a normal distribution, what percentage of beagles live more than 14 years?

0.0401

P(Z<-1.48)

0.0694

P(Z>1.48)

0.0694

the probability of randomly selecting an adult in one country that is infected by a certain virus is 0.004. In tests for the virus, blood samples from 18 people are combined. What is the probability for the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus

0.070. It is not unlikely, because the probability that the combined sample will test positive is greater than 0.05

What is the standard deviation formula for binomial distribution?

the square root of n*p*q

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 35 tablets, then accept the whole batch if there is only one or none that don't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a rate of 4% defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted or will many be rejected?

0.5890. The company will accept 58.90% of the shipments and will reject 41.10% so many of the shipments will be rejected

Assume that when an adult is randomly selected, the probability that they don't require vision correction is 19%. If 7 adults are randomly selected, find the probability that fewer than 2 of them do not require a vision correction

0.604

The following data lists the number of correct and wrong dosage amounts calculated by 34 physicians. In a research experiment, a group of 18 physicians were given bottles of epinephrine labeled with a concentration of 1 mg in 1 mL solution and another group of 16 physicians was given bottles labeled with a ratio of 2 mL of 1: 1000 solution. If one of the physicians was randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label Concentration Lab, 1 mg to 1 mL Correct: 15 Incorrect: 3 Ratio label, 1 mL to 1: 1000 Correct: 4 Incorrect: 12

0.647

Suppose 10% of Americans have heart disease. If we can randomly select 10, what is the probability that at least one of them has heart disease?

0.6513

Suppose 10% of Americans have heart disease. If we randomly select 10 Americans what is the probability that at least one of them has heart disease. Round to 4 decimal places

0.6513

Find the area of the shaded region. The graph depicts the standard normal distribution of the bone density scores with mean=0 and standard deviation=1 z=-0.85 and 1.27

0.7003

Malaria is responsible for about 40% of all hospitalizations of children under five years old in Malawi according the the President's Malaria Initiative. If twelve hospitalized children five years and under are randomly selected from Malawian hospitals what is the probability that five or less of them are hospitalized for malaria?

0.715

Suppose 12% of Americans smoke. If we randomly select 10 Americans, what is the probability that at least one of them smokes? Round to 4 decimal places

0.7215

Find the probability that when a couple has two kids, at least one of them is a boy (Assume that boys and girls are equally likely)

0.75

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 z=-0.96

0.8315

Assume that random guesses are made for 7 multiple choice questions on a medical admissions test, so that there are n=7 trials each with a probability of success (correct) given by p=0.20. Find the probability that the number x of correct answers is fewer than three

0.852

Suppose the probability that a student does not own a car is 0.12. If 15 students are selected what is the probability that at least one of them does not own a car?

0.853

Find the area of the shaded region. The graph to the right depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 75 and 120

0.8607

P(-1.48 < Z < 1.48)

0.8612

P(Z > z0) = 0.1320

0.8680

P(Z < 1.25)

0.8944

Listed below are the amounts of mercury (in parts per million or ppm) found in tuna sushi samples at different stores. The sample mean is 1.053 ppm and the sample standard deviation is 0.207 ppm. Use technology to construct a 90% confidence interval estimate of the mean amount of mercury in the population. Round to 3 decimal places

0.901 < u < 1.205

Refer to the sample data in the table below. Assume one of the 560 test subjects is randomly selected. Find the probability of selecting someone who doesn't use drugs. Does the result appear to be reasonable as an estimate of the actual proportion of the adult population that doesn't use drugs, 0.907 Uses drugs Postive: 45 Negative: 6 Does not use drugs Postive: 23 Negative: 486

0.909. Since the probability is about the same as the actual proportion of 0.907 the result is a reasonable estimate

John randomly selected 15 M and Ms and weighed them. Below are the results: 0.92, 0.99, 1.07, 0.98, 0.94, 0.98, 0.92, 0.99, 1.00, 1.01, 0.93, 1.10, 1.05, 0.94, 0.94. Create a frequency distribution with a class start of 0.92 and a class width of 0.04. Find a frequency distribution

0.92-0.95: 6 0.96-0.99: 4 1.00-1.03: 2 1.04-1.07: 2 1.08-1.11: 1 This is a skewed right distribution because the frequencies start out high and then decreases. This means the distribution is not normal

Assume that a randomly selected subject is given a bone density test. These test scores are normally distributed with a mean of 0 and a standard deviation of 1. find the probability of a bone density test score greater than -1.51

0.9345

In a genetics experiment on peas, one sample of offspring contained 387 green peas, and 19 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result close to the value of 3/4 that was epected

0.953. No, it is not reasonably close

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation 15. Find the probability that a randomly selected adult has an IQ less than 132

0.9641

What is the standard deviation equation?

the square root of the variance

Susie wants to know the effect of different colors of light on the growth of plants. She believes that plants can survive best in white light. She buys 25 ferns of the same species, which are all approximately the same age and height. She places five in white light, five in blue light, five in green light, five in red light and five in the closet. All of the ferns are planted in Miracle-Grow and given 20 mL of water once a day for 2 weeks. After that, Susie observes the plants and takes measurements. This is an example of

A completely randomized design

What is a parameter?

A number that describes the population?

How does sampling bias occur?

A sample systematically favors certain parts of the population over others

What is the point estimate of a parameter?

A single number (statistic) calculated from a random sample of units

Which of the following is not true concerning a statistic?

A statistic will always be the same as the parameter it is estimating

Instructors teaching research methods are interested in knowing what study techniques their students are utilizing. Rather than assessing all students, the researchers randomly select 10 students form each of the sections to comprise their sample. This is an example of

A stratified random sample

To determine how the weight of a vehicle impacts the gas mileage, Ann randomly select 10 compact cars, 10 midsized cars, 10 SUVS, 10 vans and 10 trucks and records the weight in pounds and the gas mileage in miles per gallon for each of the vehicles. The unit is

A vehicle

During the turn of the last century, the percentage of people with blue eyes stood at 57.4% for those born between 1899 through 1905 and 33.8% for those born between 1936 though 1951, now only 155 of people in the US have blue eyes. If 8 individuals are randomly selected A) Find the probability that at least six have blue eyes B) Find the probability that at least six DO NOT have blue eyes C) Would it be unusual for at least six individuals to have blue eyes?

A) 0 B) 0.895 C) Yes, it would be unusual as the probability of this happening would be almost 0

Assume that body temperatures are normally distributed with a mean of 98.20 and a standard deviation of 0.62. A) A hospital uses 100.6 degrees F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 degrees F is appropriate? B) Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it?

A) 0.0001. Yes, because there is a small probability that a a normal and healthy person would be considered to have a fever b) 99.22 degrees F

In 2010, 6% of adults had heart disease in the US. Answer the questions below using this percent. Create a tree diagram to illustrate all potential outcomes concerning heart disease for randomly selecting two adults from the US. A) Use the tree diagram to calculate the probability of drawing two adults with heart disease B) use the tree diagram to calculate the probability of drawing exactly one adult with heart disease C) Use the tree diagram to calculate the probability of drawing at most one adult with heart disease D) Use the tree diagram to calculate the probability of drawing at least one adult with heart disease E) If 10 adults from the US are randomly selected, what is the probability that at least one of them has heart disease?

A) 0.0036 B) 0.1128 C) 0.9964 D) 0.1164 E) 0.4614

the lengths of pregnancies are normally distributed with a mean of 270 days and a standard deviation of 15 days. A) What is the probability that a pregnancy will last 309 days or longer? B) Babies that are born on or before ____days are considered premature. (If length of pregnancy is in lowest 2% it is considered premature)

A) 0.0047 B) 239

The diabetes rate in the US is 10% based on this rate, find the following rounded to three decimal places a) If 25 people from the US were selected at random, w hat is the probability that five of them have diabetes? B) If 15 people in the US were selected at random, what is the probability that fewer than six of them had diabetes? C) If 14 people the US were selected at random, what is the probability that at least 12 of them did not have diabetes? D) If 20 people from the US were selected at random, find the mean and the standard deviation for the number that would have diabetes

A) 0.065 B) 0.998 C) 0.842 D) Mean=2 Standard deviation=1.342

Nauru formally known as Pleasant Island has the highest prevalence of diabetes in the world. Approximately 31% of adults have diabetes. Suppose we randomly select two adults from Nauru. Create a tree digram and answer the questions that follow A) what is the probability that both adults have diabetes B) What is the probability that one adult has diabetes and the other doesn't? C) What is the probability that at least one adult has diabetes? D) If we randomly select 10 adults, what is the probability that at least one of them has diabetes?

A) 0.0961 B) 0.4278 C) 0.5239 D) 0.9755

According to the national Vital Statistics, full term babies' birth weights are approximately normally distributed with mean of 7.5 pounds and standard deviation of 1.1 pounds. Some physicians believe that a bit weight of 5.5 pounds or less is dangerous. A) For a randomly selected full term pregnancy, what is the probability that the baby's birth weight is 5.5 pounds or less? B) For a randomly selected full term pregnancy, what is the probability that the baby's birth weight is between 7.2 pounds and 8.2 pounds C) if 25 full term pregnancies are randomly selected, what is the probability that the average birth weight is less than 5.5 pounds D) What is the cut off for the birth weight of babies that fall in the top 15% of birth weights? E) What is the 90th percentile for birth weights of full term babies?

A) 0.1003 B) 0.3453 C) 0.0001 D) 8.644 pounds E) 8.908 pounds

Refer to the table below. Given that 2/211 subjects are randomly selected, complete parts (a) and (b). O blood type Rh+: 70 Rh-: 9 A blood type Rh+: 67 Rh-: 9 B blood type Rh+: 26 Rh-: 4 AB blood type Rh+: 24 Rh-: 2 A) Assume that the sections are made with replacement. What is the probability that the two selected subjects are both group A and type Rh+ B) Assume the selections are made without replacement. What is the probability that the two selected subjects are both group A and Rh+?

A) 0.1008 B) 0.0998

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If two unique students are chosen at random A) What is the probability that both have brown eyes? B) What is the probability that the first student has blonde hair and the second has brown hair?

A) 0.103 B) 0.122

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If two students are chosen at random with replacement: A) What is the probability that both have brown eyes? B) What is the probability that the first student has blonde hair and the second student has brown hair?

A) 0.104 B) 0.121

Assume sugar consumption per person per year in the US is normally distributed with a mean of 150 pounds with a standard deviation in 40 pounds. If an American is chosen at random A) What is the probability that they consume more than 200 pounds of sugar per year? B) What is the probability that they consume between 100 and 200 pounds of sugar per year? For this problem, label the normal curve including the mean of 150, the values of 100 and 200 and the probability

A) 0.1056 B) 0.7888

It is generally recognized as wise to backup a computer. Assume that there is an 11% rate of disk failure in a year A) The probability that a single drive fails during a year B) The probability that both drives fail during a year is C) The probability that all three drives fail during a year is D) Describe the improved reliability that is gained with backup drives

A) 0.11 B) 0.0121 C) 0.001331 D) The probability of total data loss is substantially reduced by adding backup drives

Multiple choice questions each have four possible answers, one of which is correct. Assume that you guess on three such questions A) Use multiplication rules to find P(WWE) where C denotes a correct answer and W denotes a wrong answer B) Beginning with WWC, make a complete list of the different possible arrangements of one correct answer and two wrong answers, then find the probability for each entry in the list C) Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

A) 0.140625 B) P(WWC)= 0.140625 P(WCW)=0.140625 P(CWW)=0.140625 C) 0.421875

A researcher was interested in the effects of exercise on academic performance in elementary school children. She went to the recess area of an elementary school and identified some students who were exercising rigorously and some who weren't. She then compared the grades of the two groups. This is an example of an

Observational study

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If two unique students are chosen at random A) What is the probability that one has brown eyes and the other has green eyes? B) What is the probability that one has brown hair?

A) 0.145 B) 0.498

Choose a postmenopausal woman at random. The probability is 0.40 that the woman chosen has osteopenia (low bone density) and 0.07 that she has osteoporosis (pathological bone density). Other her bone density is considered healthy a) If two postmenopausal women are randomly selected, what is the probability that both have osteopenia? B) If two menopausal women are randomly selected, what is the probability that the first first one selected has osteopenia and the second one selected has a healthy bone density C) If two postmenopausal women are randomly selected, what is the probability that one has osteopenia and the other has a healthy bone density? D) If 15 postmenopausal women are randomly selected, what is the probability that at least one of them has osteoporosis? E) If 5 postmenopausal women are randomly selected, what is the probability that at least one of them has a healthy bone density?

A) 0.160 B) 0.212 C) 0.424 D) 0.663 E) 0.977

In 2012, approximately 9% of Oklahomans were American Indians. Answer the questions below based on this percent because the population is so large, you can assume independence and don't have to worry about adjusting the probabilities on the second random selection. A) If two oklahomans are randomly selected, what is the probability that one of them will be an American Indian and other will not? B) If two oklahomans are randomly selected, what is the probability that at least one of them is an American Indian? C) If six Oklahomans are randomly selected, what is the probability that at least one of them is an American Indian?

A) 0.1638 B) 0.1719 C) 0.4321

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If a student is chosen at random: A) What is the probability that they will have blue eyes and brown hair? B) What is the probability that a student with red hair that has green eyes is selected? C) What is the probability that they have green eyes? D) What is the the probability that the student does not have green eyes?

A) 0.171 B) 0.054 C) 0.225 D) 0.775

Although rarely diagnosed approximately 80% of Americans have some form of Candida. Use 80% as the correct percentage in your calculations. If 20 Americans are randomly selected, what is the probability that A) Exactly 15 of them have candida B) Exactly 3 of them do not have candida C) At most 15 of them have candida D) More than 10 of them have candida

A) 0.175 B) 0.205 C) 0.588 D) 0.998

Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 42​% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Complete parts​ (a) and​ (b) below. A) Find the probability that both generators fail during a power outage B) Find the probability of having a working generator in the event of a power outage. Is this probability high enough for the hospital? Assume that hospitals need both generators to fail less than 1% of the time when needed.

A) 0.1764 B) 0.8236. No because both generators fail about 18% of the time they are needed. Given the importance of the hospital's needs, the reliability should be improved

There is increasing controversy over the use of mammograms to detect breast cancer. A study found that mammograms were found to give incorrect results 75% of the time. Suppose two women receive mammograms. (Since the population we are drawing from is large, we can assume independence and use the multiplication rule for independent events) A) What is the probability that the first obtain correct results and the second obtained incorrect results? B) What is the probability that one obtained correct results and the other obtained incorrect results?

A) 0.1875 B) 0.375

A genetic experiment with peas resulted in one sample of offspring that consisted of 426 green peas and 156 yellow peas A) Construct a 955 interval to estimate the percentage of yellow peas B) Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?

A) 0.232 < p < 0.304 B) No, the confidence interval does not include 0.25, so that true percentage could easily equal 25%

The accompanying table describes results from 8 offspring peas. The random variable x represents the number of offspring peas with green pods. 0 peas with green pods=0+ 1 pea with green pods=0+ 2 peas with green pods: 0.005 3 peas with green pods: 0.025 4 peas with green pods: 0.087 5 peas with green pods: 0.236 6 peas with green pods: 0.279 7 peas with green pods: 0.252 8 peas with green pods: 0.116 A) Find the probability of getting exactly 7 peas with green pods B) find the probability of getting 7 or more peas with green pods C) Which probability is relevant for determine whether 7 is an unusually high number of peas with green pods? D) Is 7 an unusually high number of peas with green pods? Why or why not? Use 0.05 as the threshold for an unusual event

A) 0.252 B) 0.368 C) The rest from part b D) No, since the appropriate probability is greater than 0.05, it is not an unusually high number

A survey of commercial poultry raising operations was conducted to determine the extent to which rodents are a nuisance in poultry houses. The surveyed houses were classified into two types (chicken and turkey) and the extent of the rodent infestations was recorded as mild, moderate, or severe. In the table below is a breakdown of the type of operation and the severity of rodent problem. Chicken Mild: 34 Moderate: 33 Severe: 7 Total: 74 Turkey Mild: 22 Moderate: 22 Severe: 4 Total: 48 If we randomly select one of these poultry operations, find the probability of the operation A) Is a turkey operation B) Does not have a severe rodent problem C) Is a chicken operation and has moderate rodent problems D) Is a turkey operation OR has severe rodent problems

A) 0.3934 B) 0.9098 C) 0.2705 D) 0.4508

What is a completely randomized design?

the treatments are assigned to all the experimental units completely by chance

Refer to the table below to answer questions below. Round all to four decimal places O blood type Rh+: 71 Rh-: 21 A blood type Rh+: 60 Rh-: 18 B blood type Rh+: 32 Rh-: 7 AB blood type Rh+: 14 Rh-: 8 A) what is the probability that a randomly selected person from the subjects represented has O blood B) What is the probability that a randomly selected person from the subjects presented in the chart has O+ blood? C) wHat is the probability that a randomly selected person from the subjects presented on the chart has type A or Rh+ blood? D) What is the probability that a randomly selected person has type A blood given they are Rh+ E) What is the probability that a randomly selected person has Rh+ blood, given they are type A F) If two unique individuals are randomly selected, what is the probability that the first one has AB blood and the second has B blood? G) If two unique individuals are randomly selected what is the probability that one has AB blood and the other has B blood?

A) 0.3983 B) 0.3074 C) 0.8442 D) 0.3390 E) 0.7692 F) 0.0161 G) 0.0323

The table below show the effectiveness of experimental antivenin for scorpion stings in children No Improvement Antivenom: 1 Placebo: 6 Total: 7 Improvement Antivenom: 7 Placebo: 1 Total: 8 A) If one child is chosen at random, what is the probability they received the placebo and had no improvement? B) If one child is chosen at random, what is the probability that they received the antivenin given they experienced no improvement? C) If one child is chosen at random, what is the probability they received a placebo? D) If one child is chosen at random what is the probability they received a placebo or had no improvement? E) If two unique children are chosen at random, what is the probability that one of them received the placebo and the other received the antivenom? F) If two unique students are chosen at random, what is the probability that both of them received the placebo? G) If two unique children are chosen at random, what is the probability that the first one selected received the placebo and the second one received the antivenom

A) 0.4 B) 0.1429 C) 0.4667 D) 0.5333 E) 0.5333 F) 0.2 G) 0.2667

Below is a two way table showing the relationship between type of food preference and gender. Savory Male: 28 Female: 15 Total: 43 Sweet Male: 22 Female: 35 Total: 57 A) if a person is randomly selected, what is the probability that they will prefer savory food? B) If a person is randomly selected what is the probability they will be female and prefer sweet food? C) If a person is randomly selected, what is the probability they will be female or prefer sweet food? D) If a person is randomly selected what is the probability that they will be female given they prefer sweet food? E) If a person is randomly selected what is the probability that why prefer sweet food given they are female? F) If two unique people are randomly selected, what is the probability that they both prefer sweet food? G) If two unique people are randomly selected, what is the probability that the first prefers sweet food and the second savory food? H) If two unique people are randomly selected, what is the probability that one of them prefers sweet food and the other savory food?

A) 0.43 B) 0.35 C) 0.72 D) 0.61 E) 0.70 F) 0.3224 G) 0.2476 H) 0.4952

Assume sugar consumption per person per year in the US is normally distributed with a mean of 150 pounds and a standard deviation of 40 pounds. A) If a single person is selected, what is the probability that they consume on average more than 155 pounds of sugar? B) If a simple random sample of 100 individuals in the US is taken what is the probability that this group consumes on average more than 155 pounds? C) If a simple random sample of 100 individuals in the US is taken what is the probability that this group consumes on average between 145 and 160 pounds?

A) 0.4483 B) 0.1056 C) 0.8882

A survey of commercial poultry raising operations was conducted to determine the extent to which rodents are a nuisance in poultry houses. The surveyed houses were classified into two types (chicken and turkey) and the extent of the rodent infestations was recorded as mild, moderate, or severe. In the table below is a breakdown of the type of operation and the severity of rodent problem. Chicken Mild: 34 Moderate: 33 Severe: 7 Total: 74 Turkey Mild: 22 Moderate: 22 Severe: 4 Total: 48 If we randomly select one of these poultry operations, find the probability of the operation A) If a poultry operation is randomly selected, what is the probability it has mild problems given it is a chicken operation? B) If the poultry operation is randomly selected, what is the probability it is a turkey operation given it has severe problems? If we randomly select two of these poultry operations with replacement C) What is the probability that both are chicken operations? D) What is the probability that the first one selected is a chicken operation with moderate problems and the second one selected is a turkey operation with severe problems? If we randomly select two of these poultry operations without replacement E) What is the probability that both are chicken operations? F) What is the probability that the first one is a chicken operation with moderate problems and the second one selected is a turkey operation with severe problems?

A) 0.4595 B) 0.3635 C) 0.3679 D) 0.00887 E) 0.3659 F) 0.00894

in the week before and the week after a holiday, there were 10,000 total deaths, and 4963 of them occurred in the week before the holiday (a) construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday (b) based on the results, does there appear to be any indication that people can temporarily postpone their death to survive the holiday?

A) 0.487 < u < 0.506 B) No, because the proportion could easily be 0.5. The interval is not less than 0.5 the week before the holiday

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If a student is chosen at random: A) What is the probability that they have blue eyes or blonde hair? B) What is the probability that the student has red hair or green eyes?

A) 0.527 B) 0.318

In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 12 people are randomly selected A) Find the probability that all the selected people have brown eyes B) Find the probability that exactly 11 of the selected people have brown eyes C) Find the probability that the number of selected people that have brown eyes is 10 or more D) If all 12 people are randomly selected, is it unusual for a 10 or more to have brown eyes?

A) 0.540 B) 0.341 C) 0.980 D) No, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05

In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 12 people are randomly selected. A) Find the probability that all selected people have brown eyes B) What is the probability that exactly 11 of the selected people have brown eyes C) Find the probability that the number of selected people that have brown eyes is 10 or more D) If 12 people are randomly selected, is 10 an unusually high number for those with brown eyes?

A) 0.540 B) 0.341 C) 0.980 D) No, because the probability that 10 or more of the selected people have brown eyes is greater than 0.05

There is increasing controversy over the use of mammograms to detect breast cancer. A study found that mammograms were found to give incorrect results 75% of the time. Suppose two women receive mammograms. (Since the population we are drawing from is large, we can assume independence and use the multiplication rule for independent events) A) What is the probability that both obtain incorrect results? B) What is the probability that the first selected woman obtained correct results and the second selected women contained incorrect results?

A) 0.5625 B) 0.1875 C) 0.0352

Suppose we have a group of 3 males and 4 females. Assume no replacement. Create a tree diagram for randomly selecting two individuals The chance of selecting a male is 3/7 and the chance of selecting a female 4/7. A) What is the probability that we randomly select one of each? B) What is the probability that we randomly select at least one male when randomly selecting two individuals? C) What is the probability that we randomly select at least one male when randomly selecting three individuals?

A) 0.5714 B) 0.7143 C) 0.8857

Assume that women's heights are normally distributed with a mean given by 63.7 inches and a standard deviation is given by 1.6 inches A) If one woman is randomly selected, find the probability that her height is less than 64 inches B) if 36 women are randomly selected, find the probability that they have a mean height of less than 64 inches

A) 0.5753 B) 0.8708

Data was collected from 160 subjects. The type of diet they were on and whether or not they completed the diet was recorded. Use the table to answer the questions that follow: Zone Completed: 25 Did not complete: 13 Total: 38 Weight watchers Completed: 27 Did not complete: 15 Total: 42 Ornish Completed: 18 Did not complete: 19 total: 37 Atkins Completed: 23 Did not complete: 20 total: 43 A) If one subject is selected at random, what is the probability that they completed the diet? B) If one subject is selected at random, what is the probability that they were on the Atkins diet? C) If one subject is selected at random, what is the probability that they were on the Atkins diet and completed it? D) If one subject is selected at random, what is the probability that they were on the Atkins diet or completed the diet they were on? E) If one subject is selected at random, what is the probability that they completed the diet given they were on the Atkins diet? F) If one subject is selected at random, what is the probability that they were on the Atkins diet given they completed their diet? G) If two unique subjects are selected at random, what is the probability they were both on the Zone diet? H) If two unique subjects are selected at random, what is the probability that the first one was on the Zone diet and the second was on the Atkins diet? I) If two unique subjects are selected at random, what is the probability that one was on the Zone diet and the other on the Atkins diet? J) If 10 subjects are selected at random with replacement what is the probability that at least one of them completed their diet?

A) 0.581 B) 0.269 C) 0.144 D) 0.706 E) 0.535 F) 0.247 G) 0.055 H) 0.064 I) 0.128 J) 0.9998

Assume that females have pulse rates that are normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute. A) If 1 adult is randomly selected, find the probability that her pulse rate is less than 76 beats per minute B) If 16 adult females are selected, find the probability that they have pulse rates with a mean less than 76 beats per minute C) Why can the normal distribution be used in part b even though the sample size doesn't exceed 30?

A) 0.5948 B) 0.8315 C) Since the original population has a normal distribution, the distribution of sample means is a normal distribution

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 and 191 pounds. The new population of pilots has normally distributed weights with a mean of 140 pounds and a standard deviation of 28.2 pounds. A) If a pilot is randomly selected, find the probability that his weight is between 130 and 191 pounds B) If 33 different pilots are randomly selected, find the probability that their mean weight is between 130 and 191 pounds C) When redesigning the ejection seat, which probability is more relevant?

A) 0.6017 B) 0.9792 C) Part a because the seat performance for a single pilot is more important

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If a student is chosen at random: A) what is the probability that the student has blue eyes or green eyes? B) What is the probability that the student has red hair or black hair?

A) 0.678 B) 0.279

Listed below are the measured radiation emission (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J and K respectively. The media often presents reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. 0.87, 1.03, 0.78, 0.22, 0.57, 1.31, 0.42, 0.97, 1.44, 0.64, 0.31 A) Find mean B) Find median C) Find midrange D) Find the mode E) If you were planning to purchase a cell phone, are any of these measurement the most important statistic? Is there another statistic that is most relevant? If so, which one?

A) 0.788 B) 0.780 C) 0.830 D) There is no mode E) The max data value is the most relevant statistic because it is closest to the limit of 1.6 W/kg and that cell phone should be avoided

Black hair and blue eyes: 4 Black hair and brown eyes: 28 Black hair and green eyes: 2 Total: 34 Blonde hair and blue eyes: 50 Blonde hair and brown eyes: 6 Blonde hair and green eyes: 13 Total: 69 Brown hair and blue eyes: 44 Brown hair and brown eyes: 44 Brown hair and green eyes: 29 Total: 117 Red hair and blue eyes: 19 Red hair and brown eyes: 5 Red hair and green eyes: 14 Total: 38 Answer the questions that follow and round all answers to three decimal places. If a student is chosen at random: A) What is the probability that the person has brown eyes given that they have black hair? B) What is the probability that the person has blonde hair given they have green eyes?

A) 0.824 B) 0.224

Find range, variance, and standard deviation, include appropriate units in results. Listed below are then measured radiation absorption rates (in W/kg) corresponding to various cell phone models. If one of each model is measured for radiation and the results are used to find measures of variation, are the results typical of the population of cell phones that are in use? 0.66, 1.25, 0.91, 1.07, 0.61, 0.77, 0.99, 1.44, 1.16, 1.39 and 0.87 A) The range is B) Sample standard deviation C) Sample variance D) Are the results typical of the population of cell phones that are in use?

A) 0.830 W/kg B) 0.286 W/kg C) 0.82 (W/kg)^2 D) No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighed according to the size in the population

The height of a certain population of corn plants follow a normal distribution with a mean of 150 cm and a standard deviation of 2.4 cm. Round to 4 decimal places A) What is the probability that a randomly selected corn plant from this population is between 145 and 169 cm tall? B) What is the probability that a randomly selected plant from this population is less than 145 cm tall? C) Suppose a random sample of 16 corn plants is taken from this population. What is the probability that their average height is above 155 cm? D) What height would a corn plant in the 80th percentile have? E) What height would a corn plant have that was in the top 30% of corn plants? Round to two decimal places?

A) 0.9811 B) 0.0188 C) 0.0001 D) 152.02 E) 151.25

If X ~ N(4, 1.5), first standardize and then find the following probabilities A) Find P(X < 8) B) Find P(X > 7) C) Find P(3 < X < 7) D) Find P(X=3.45) E) Find P(x > 11)

A) 0.9962 B) 0.0228 C) 0.7258 D) 0 E) 0.0001

You want to estimate the percentage of adults who believe that passwords should be replaced with biometric security (such as fingerprints). How many randomly selected adults must you survey? Assume that you want to be 95% confident that the sample percentage is within 2.8 percentage points of the true population percentage. A) Assume that nothing is known about the percentage of adults who believe that passwords should be replaced with biometric security B) Assume that a prior study suggests that 47% of adults believe that biometric security should replace passwords C) Does the additional survey information from part b have much of an effect on the sample size that is required?

A) 1226 B) 1221 C) The additional survey information from part b causes the required sample size to change by less than 10%. Based on this, the additional survey information causes no significant change in the sample size that is required.

The average life expectancy of a beagle is 13.3 years with standard deviation 0.4 years. Assuming that the life expectancies follow a normal distribution, A) the beagles with the highest 10% of life expectancies live how many years? B) What is the 70th percentile for life expectancies of beagles?

A) 13.812 years B) 13.508 years

Find the sample size needed to estimate the percentage of residents of one region of a country who are left handed. Use a margin of error of two percentage points, and use a confidence level of 90% A) Assume that p hat and q hat are unknown. The sample side needed is (Round up to the nearest whole number) B) Assume that based on prior studies, about 14% of residents of the region are left handed C) How do the results from parts a and b change if the entire country is used instead of one region of that country?

A) 1692 B) 815 C) If the entire country is used instead of one region, the results from parts a and b don't change

and group 4 were asked to exercise for 20 minutes per day and eat a low sugar diet. Their blood pressure was taken before and after the experiment A) How many factors are there and what do they include? B) Exercising 20 minutes per ay and eating a regular diet is a C) How many treatments are there? D) The 100 volunteers are the

A) 2 and exercise/diet and diet/exercise B) treatment C) 4 D) Subjects

To determine the average number of times students in fifth grade at Will Rogers Elementary School go to the dentist, a school separates students into four groups based on race (Caucasian, African American, Hispanic and Other) and randomly selects 10 students from each group. Each student is asked how many times they have gone to the dentist in the last year. A) Which of the following is true concerning this study? 1. The sample size is 10 2. A sample of only Caucasians is possible as there are a greater number of Caucasians at Will Rogers 3. The person conducting the study thinks that the number of dentist visits will differ depending on the child's race 4. None of the above are true B) The type of sampling design used for this study is C) To decrease variability in our statistic, which of the following would work best? D) Hospital A has a higher death rate than hospital B. This is because hospital A takes patients with more serious conditions. The condition of the patients at the respective hospitals make hospital B look better. This is an example of

A) 3 B) Stratified random sample C) Increase sample size D) Common response and a lurking variable

You have been given the task of estimating the percentage of SW flights that arrive on time, which is no later than 15 minutes after the schedule arrival time. How many flights must you survey in order to be 90% confidence that your estimate is within three percentage points of the true population percentage A) Assume that for a recent year, 84% of SW flights were on time B) If no previous study had been done, what sample size would be needed?

A) 405 B) 752

If X~N(3,1.5), find x0 for each of the following A) P(X<x0)=0.95 B) P(X>x0) C) find P30 which is the value separating the top 30% from the top 70%

A) 5.4675 B) 0.855 C) 2.22

Below is a random sample of life expectancies from 20 countries: 70, 65, 70, 51, 57, 61, 78, 61, 72, 64, 56, 73, 69, 52, 78, 54, 74, 76, 70, 68. Make a frequency table of the life expectancies with a starting lower class limit of 50 and a class width of 5. Answer the following questions based on that table A) What are the class midpoints? B) What are you lower class limits? C) what are your upper class limits?

A) 52, 57, 62, 67, 72, 77 B) 50, 55, 60, 65, 70, 75 C) 54, 59, 64, 69, 74, 79

You are given a 50 point multiple choice final with 5 choices for each question. If you did not study like an idiot and had to guess on every question, what is the probability that you will get 60% on the exam? A) What is your trial? B) What would be considered a success? C) What is the probability of obtaining a 60% D) What is the mean and standard deviation for the distribution of correct answers? E) What is the range for usual values obtained from just guessing

A) Guessing on one multiple choice question B) Guessing correctly C) 0 D) mean= 10 and standard deviation is 2.83 E) 4.34 to 15.66

You want to estimate the percentage of adults who believe that passwords should be replaced with biometric security (such as fingerprints). How many randomly selected adults must you survey? Assume that you want to be 95% confident that the sample percentage is within 4.1 percentage points of the true population percentage. A) Assume that nothing is known about the percentage of adults who believe passwords should be replaced with biometric security. The sample size needed is (round up to the nearest whole number) B) Assume that a prior study suggests that about 46% of adults believe that biometric security should replace passwords C) Does the additional survey from part (b) have much of an effect on the sample size required?

A) 572 B) 568 C) The additional survey information from part b causes the required sample size to change by less than 10%. Based on this, the additional survey information causes no significant change in the sample size that is required

Several psychology students are unprepared for a surprise true/false test with 15 questions and all their answers are guesses A) Find mean B) Find standard deviation C) Would it be unusual for a student to pass by guess (at least 13 questions need to be correct). Why or why not?

A) 7.5 B) 1.9 C) Yes, because 13 is greater than the maximum usual value

Assume that the given procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value mean-2(standard deviation) and the maximum usual value mean + 2(standard deviation). In an analysis of preliminary test results from a gene selection method, 19 babies are born, and it is assumed that 50% of babies are girls, so n=19 and p=0.5 A) The value of the mean is B) The value of the standard deviation is C) The minimum usual value is D) The minimum usual value is

A) 9.5 B) 2.2 C) 5.1 D) 13.9

A random sample of 10 temperatures was taken from high temperatures of July 2014. The values are listed below: 91, 96, 71, 102, 99. 85, 97, 97, 103, 101 A) What is median? B) IQR C) Five number summary D) Outliers? E) Mean F) Standard deviation

A) 97 B) 10 C) 71, 91, 97, 101, 103 D) 71 E) 95.51 F) 9.77

To determine whether a new type of mattress will cut down on the number of bed sores, a nursing home randomly assigns 10 bed ridden patients to the new mattress and 10 bed ridden patients to the old mattress. After 10 weeks they examine the 20 patients to determine if they have any new bed sores and compare the results for the two groups A) This is an example of a B) The factors for this study are

A) A completely randomized experiment B) type of mattress

John wanted to estimate the average literacy rate for all countries. He randomly selected 35 countries and researched the literacy rate for each a) The statistical unit for John's study is B) The population John is interested in calculating an estimate for is C) Suppose John plugged his data into SPSS and calculated a sample mean of 82% and a 90% confidence interval of (78%,86%). Find the center of the confidence interval by adding the two end points and dividing by 2. wHat value did you calculate? D) No matter how many times we calculate our sample mean and confidence interval, the sample mean will always be exactly in the middle of our confidence interval. That is because we use the sample mean as the center point of the confidence interval. Notice that we take out sample mean and subtracting and adding the same amount to get the two endpoints of our confidence interval. This means we are E) So what is John only 90% confident of?

A) A country B) All countries in the world C) 82% (Same value as his sample mean) D) 100% confident that our sample mean is exactly in the middle of our confidence interval E) John is 90% confidence that his confidence interval (78%, 86%) captures the population mean literacy rate for all countries

In a survey of 1121 adults in the US, 49% said that they washed their hands after riding public transportation. A) Identify popualtion B) Identify sample C) Is the value of 49% a statistic or parameter?

A) All adults in the US B) The 1121 adults surveyed C) A statistic because it describes a characteristic of a sample

A researcher in New York wants to determine the proportion of people living near high power lines that have cancer. To do this, he randomly selected 50 individuals from New York who live near high power lines and records whether or not they have cancer. A) The unit for this study is B) The response variable for this problem is C) Suppose some of the individuals living near high power lines did not make it into the list the researcher sample from. what type of bias could have occurred?] D) Suppose only 40 of the 50 individuals responded. What type of bias could have occurred?

A) An individual living near high power lines in New York B) Whether or not an individual has cancer. It is categorical or qualitative C) Undercoverage D) nonresponse

What does a confidence interval include?

A) An interval computed from the sample B) A confidence level

Each of the two parents has a genotype of blue/brown, which consists of a pair of alleles that determine eye color and each parent contributes one of those alleles to a child. Assume that If the child has at least one blue allele, that color will dominate and the child's eye color will be blue. A) List all possible outcomes B) The probability of these parents having a child with the brown/blue genotype is C) The probability that the child will have blue eye color is

A) BB, Bb, bB, bb B) 0.25 C) 0.75

Each of two parents has the genotype brown/blue. which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. A) List the different possible outcomes B) Assume that these outcomes are equally likely. How many simple events do you have? C) Is both parents contributing blue alleles a simple or compound event? D) Is one parent contributing a blue alleles and one parent contributing a brown allele a simple event or compound event? E) What is the probability that a child of these parents will have brown eyes?

A) Bb, bB, BB, bb B) 4 C) simple event D) compound event E) 1/4

According to the national vital statistics, full term babies' birth weights are approximately normally distributed with mean of 7.5 pounds and standard deviation of 1.1 pounds A) Between what values do the middle 68% of all full term babies' birth weights fall? B) What percent of births weights are between 7.5 pounds and 9.7 pounds

A) Between 6.4 and 8.6 pounds B) 47.5%

A study is conducted to measure​ children's growth rates without any treatment applied to the children. What best classifies this​ study?

Observational study

Assume that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 30. Complete parts​ (a) through​ (c) below. a) The value of the mean is u=_____. The value of the standard deviation is o=_____. b) Values of _____ peas or fewer are significantly low. Values of _____ peas or greater are significantly high. c) The result _____ significantly low, because 8 peas with green pods is __________ _____ peas.

A) Mean=22.5 Standard deviation=2.4 B) 17.7, 27.3 C) is, less than 17.7

A health care provider wants to rate its members' satisfaction on a scale of 1 to 10, 10 being most satisfied. A survey is mailed to 300 randomly chosen members of this health plan. Only 89 surveys were returned. Identify (a) response variable, (b) unit, (c) population and (d) sample

A) Members satisfaction on a scale of 1 to 10 B) Member of heath plan C) All members of health plan D) 89 members that responded

Determine whether the study is an experiment or an observational study, and then identify a major problem with the study. A medical researcher tested for a difference in blood pressure levels between male and female students who are 12. She randomly selected 4 males and 4 females A) This is an ____ because the researcher ____ the individuals B) What is the major problem with the study?

A) Observational study, does not attempt to modify B) The sample is too small

A poll interviewed by phone a random sample of 500 adults in Oklahoma, 350 said that smoking in public places should be banned A) What is the population studied and what parameter are we interested in? B) Give the numerical value of the statistic p hat that estimates p C) Give a 95% confidence interval for the proportion of adults who think that smoking in public should be banned D) Describe the confidence interval in words E) Was it appropriate to find the confidence interval?

A) Population: All adults in Oklahoma Parameter: Proportion of adults in Oklahoma who think smoking should be banned in public B) 0.7 C) (0.66,0.74) D) There is a 95% confidence that the interval 0.66 to 0.74 captures the proportion of all adults in oklahoma who think that smoking should be banned in public places E) Yes, the number of successes and the number of failures are both at least five

During the turn of the last century, the percentage of people with blue eyes stood at 57.4% for those born between 1899 through 1905 and 33.8% for those born between 1936 though 1951, now only 155 of people in the US have blue eyes. If 15 individuals are randomly selected A) Describe the trial in words B) Which outcome will you call a success? C) Find the probability that exactly 10 randomly selected individuals have blue eyes D) Find the probability that exactly 3 randomly selected individuals have blue eyes E) Find the probability that exactly 11 randomly selected individuals do not have blue eyes

A) Randomly selecting someone born in the US and determining whether or not they have blue eyes B) The randomly selected person has blue eyes C) 0.0000077 D) 0.218 E) 0.116

Refer to the values described below, then identify which of the following is the most appropriate: discrete random variable, continuous random variable, or neither a) Exact height of 200 puppies born in a region B) Shoe sizes C) Responses to the survey question, "Do you have children?" D) Exact head circumference of humans E) Number of people in families

A) Since the outcomes are not countable this is a continuous random variable B) Since the outcomes are countable, this is a discrete random variable C) Since the outcomes are not numerical, this is not a random variable D) since the outcomes are not countable this is a continuous random variable E) since the outcomes are countable, this is a discrete random variable

Suppose the local Childhood Lead Poisoning Prevention Council in a metropolitan area in western Tennessee undertakes the responsibility of determining the proportion of homes in their city that have unsafe lead levels. Because of the great expense involved in preforming spectrometric testing they decide to test only some of the homes. The Council assumes that houses built prior to 1970 are more likely to have unsafe lead levels. Consequently, they divide their population into homes built prior to 1970 and homes built after 1970. They then take a random sample of 100 homes from each group and record the lead levels for each home. A) What type of sample design was used? B) Suppose the lead testing equipment was faulty and some of the lead levels recorded were incorrect. What type of bias will this study suffer from? C) Suppose in the process of obtaining the population of all homes, several neighborhoods were mistakenly omitted. What type of bias will this study potentially suffer from? D) Suppose that some of the owners refused to allow the council to test their homes for lead. What type of bias will be introduced into the study

A) Stratified random sample B) response bias C) undercoverage D) nonresponse

A) List the possible outcomes if you toss a coin twice B) Is the chance of tossing two heads a simple event? C) Is the chance of tossing one head and one tail a simple event? D) What is the probability that you will toss a single head? E) What is the probability that you will toss two heads? F) What is the probability that you will toss at least one head?

A) TT, TH, HT, HH B) Yes, only one of the outcomes is two heads C) NO, more than one outcome has one head and one tail D) 1/2 E) 1/4 F) 3/4

Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous system, causing encephalopathy and ultimately death. In 2012 the breakdown of rabies among wild animals in the US was as follows Species and Probability Raccoon: 0.317 Bat: 0.273 Fox: 0.055 Skunk: 0.25 Other: 0.105 A) Are the even of obtaining a fox or the event of obtaining a bat disjoint? B) What is the probability that the reported case of rabies is a fox? C) What is the probability that the reported case of rabies is a fox or a bat?

A) Yes B) 0.055 C) 0.328

Do one pound bags of carrots actually weigh one pound? To determine this, fifty-one pound bags of carrots are selected from Sprouts and weighed. A) The units for this study is B) If we wanted to extend out results to all bags of carrots, then our study has which type of bias? C) If our scale was not working correctly, our study would have which type of bias? D) If one of the 50 bags that we randomly selected from Sprouts was lost, which type of bias could our study potentially have? E) The response variable for this study is F) The average weight of the fifty 1 pound bags of carrots is a

A) a 1 pound bag of carrots B) Undercoverage bias C) response bias D) nonresponse bias E) The weight of a 1 pound bag of carrots F) statistic

What is quantitative variable?

takes numerical values for which arithmetic operations such as adding and averaging make sense. Typically described with a dot plot, stem plot or histogram

A completely randomized design was proposed by a consumer products agency to decide which of the 3 different brands of insect repellent provides the greatest protection from mosquito bites. The three different brands are to be randomly assigned to 18 children with 6 assigned to each brand. After the repellants are applied, the children will be sent out to play on a humid summer evening. After one hour the number of mosquito bites each child received will be recorded. A) The experimental unit for this study is B) The treatments for this experiment are C) The type of experiment conducted was

A) a child B) The brands of insect repellant C) completely randomized design

To determine the average number of acres of corn planted per farm in the US, all farms are placed in three groups depending on size. A random sample of 10 farms is taken from each group. A) The unit for the study is B) The sample is C) Suppose that a farm randomly selected does not have any acres of corn planted. This would be an example of D) What type of sampling design was used in this study? E) Suppose a farmer gave the incorrect number of acres planted for his farm. what type of bias could this study suffer from?

A) a farm B) 30 selected farms C) No bias occurred D) Stratified random sample E) Response

A researchers wants to determine the total number of black bears found at yellow national park. To determine this, it is divided into 4 regions and each region is divided into 100 plots. For each region, a random sample of 10 plots is taken and the number of black on those blocks counted A) The unit is B) The sample for this study is C) The sampling designed used for this study is D) It is very difficult to count the number of bears in a plot without making a mistake, consequently, this study will have E) When listing all the plots to sample from, several plots from one region were not included on the list. This study may have

A) a plot B) the 40 randomly selected plots C) Stratified random sample D) response bias E) Undercoverage bias

Hospital floors are usually covered by bare tiles. Carpets would cut down on noise but might be more likely to harbor gems. To study the possibility, investigators randomly assigned 8 to 16 available hospital rooms to have carpet installed. The others were left bare. Later, air from each room was pumped over a dish of agar. The dish was incubated for a fixed period of time, and the number of bacteria colonies were counted for each dish. For this experiment, what are the following? A) Unit B) Factors and their levels C) Treatments D) Response variable

A) hospital floor B) type of flooring with 2 levels, tile and carpet C) Tile and carpet D) The number of bacteria colonies that are counted for each floor

When Mendel conduced his famous genetics experiment with peas, one sample of offspring consisted of 580 peas and Mendel theorized that 25% of them would be yellow peas. A) If Mendel's theory is correct, find the mean and standard deviation for the number of yellow peas in such groups of 580 offspring peas B) The actual results consisted of 152 yellow peas. Is this result unusual? What does this result suggest about Mendel's theory?

A) mean= 145 and standard deviation=10.43 B) Since 152 is contained in the interval, Mendel's results are not unusual, but were consistent with his theory suggesting that it was correct

A forester is interested in determining the total number of trees that are planted on tree farms in Montana. The forester believes the number of trees varies with the size of the tree farm. He divides all such farms into four classes depending on their size. From each class, he selects a sample of 15 farms. He counts and records the total numbers of trees for each of the selected tree farms. Identify the response variable, unit, population and sample

A) number of trees on selected tree farm B) tree farm C) all tree farms in Montana D) 60 selected tree farms

A test was done to determine which of the three diets (A, B and C) combined with two exercise programs (none and 20 minutes per day) would most improve a person's blood pressure. Sixty patients were randomly assigned to experimental groups and their blood pressure was taken before and after six weeks on the exercise/diet program. For this experiment, what are the following? A) Unit B) Factors and their levels C) Treatments D) Response variable

A) patient B) the diet with 3 levels, A, B and C. Exercise with two levels, yes and no C) Each diet with no exercise, each diet with exercise D) Change in blood pressure for the patient

What is response bias?

tendency of subjects to systematically respond to a stimulus in a particular way due to nonsensory factors

What is the midrange?

the average of the greatest and least values in the data set

Which of the following is NOT a principle of probability?

All events are equally likely to occur in any probability procedure

To determine how the weight of a vehicle impacts the gas mileage, Ann randomly select 10 compact cars, 10 midsized cars, 10 SUVS, 10 vans and 10 trucks and records the weight in pounds and the gas mileage in miles per gallon for each of the vehicles. The population is

All vehicles

What is a double blind experiment?

An experiment in which both the individuals doing the testing and being tested are unaware of the hypothesis and who is in either the experimental or control group

What is a unit?

An individual person, animal or object upon which the response variable or variable of interest is measured

What is a census?

Attempt to contact every individual in an entire population

What is the mean of a density curve?

the balance point, at which the curve would balance if made of solid material

What does non-disjoint mean?

Can happen at the same time

There is a strong correlation between cell phone use in a country and number of children per woman. This is because countries that are deathly have a higher level of cell phone use and less children per woman. This is an example of

Common response

If the scenario describes an experiment

Completely randomized design and randomized block design

The ability to grow in shade may help pines found in the dry forests of Arizona resist drought. To test this hypothesis, investigators randomly assigned 50 seedlings in a greenhouse to either full light, light reduced to 25% of normal, or light reduced to 50% of normal. At the end of the study, they dried the young trees and weighed them. What type of experimental design is this?

Completely randomized design with three treatments

What is a parameter?

Number that describes the population. It is a fixed number

The number of students who have received parking tickets. Discrete or continuous random variable?

Discrete

What is a placebo?

Dummy treatment

Units/Individuals are

Objects described by a set of data

Determine whether the given description corresponds to an observational study or experiment. In a study designed to study the effectiveness of a drug as a treatment for lower back pain, 1643 patients were randomly assigned to one of 3 groups (1) the 547 subjects in the placebo group were given pills containing no medication (2) 550 subjects were in a group given pills with the drug taken at regular intervals (3) 546 subjects were in a group given pills with the drug to be taken when needed for pain relief

Experiment because treatment was applied

What is the explanatory variable?

Explains or causes changes in the response variable

Determine whether the sampling method described below appears to be sound or flawed. Ina survey of 572 subjects, each was asked how often he or she ate bananas. The survey subjects were Internet users who responded to a question that was posted on a news website

Flawed because it is a voluntary response sample

John scored a 1200 on the SAT and a 25 on the ACT. On which test did he do better if the SAT has a mean of 1026 and a standard deviation of 209 and the ACT has a mean of 20.8 and standard deviation of 4.8?

He did better on the ACT

What is the IQR equation?

IQR=Q3-Q1

Suppose that a crime scene DNA sample was recovered and a suspect was later arrested. The DNA profiles of the crime strain and the suspect were type and both had the same DNA profile at loci D3S1358, VWA, FGA, THO1, TPOX, and CSF1P0. If both had alleles 15 and 16 from D3S1358 (0.2896 and 0.2287), 17 for VWA (0.2774) and 22 and 24 for FGA (0.2287 and 0.1463) 7 for THO1 (0.316), 8 and 11 for TPOX (0.545 and 0.313) and 10 and 11 for CSF1P0 (0.239 and 0.261), compute match probability and likelihood ratio. Explain what the likelihood ratio is telling you

Match probability: 0.000002899 LR: 344,936 There is a 1 in 344,936 chance that the blood of a random person would match the blood at the crime scene for the six loci

Suppose that a crime scene DNA sample was recovered and both the suspect and the crime strain had DNA profiles that matched. Calculate the match probability if both had allele 10 for CSF1P0 (0.239), alleles 6 and 9.3 for THO1 (0.100 and 0.029) and allele 11 for TPOX (0.313). Use information to calculate match probability and likelihood ratio

Match probability: 0.000032457 LR=30809 There is a 1 in 30809 chance that the blood of a random person off the street will match the crime strain

Suppose that a crime scene DNA strand was recovered and a suspect was later arrested. The DNA profiles of the crime strain and the suspect were typed and had the same DNA at allele 7 for THO1 (0.316), alleles 9 and 11 for TPOX (0.100 and 0.313), and alleles 11 and 13 for CSF1P0 (0.261 and 0.082), compute the match probability and LR. State likelihood in words

Match probability: 0.000268 LR: 3737 There is a a 1 in LR chance that the blood of a random person matches the blood at a crime scene at loci THO1, TPOX, CSF1P0

Suppose that a crime scene DNA sample was recovered and a suspect was later arrested. The DNA profiles of the crime strain and the suspect were typed and both had the same DNA profiles at loci THO1, TPOX and CSF1P0. If both had allele 9 for THO1 (0.440), alleles 8 and 11 for TPOX (0.545 and 0.313) and alleles 11 and 12 for CSF1P0 (0.261 and 0.362), compute the match probability and likelihood ratio using the chart. STate likelihood ratio in words.

Match probability: 0.0125 LR: 80 There is a 1 in LR chance that the blood of a random person matches the blood at the crime scene at the loci TH01, TPOX, and CSF1P0

Below is the number of tornadoes recorded each month in 2013, use SPSS and find the mean and standard deviation. Are there any unusual number of tornadoes for any of the years? 75, 39, 18, 86, 265, 122, 71, 45, 21, 57, 78, 14

Mean: 74.25 Standard Deviation: 67.993 The number of tornadoes in May, 265, is an unusual observation

Use SPSS to find the mean, standard deviation, median, interquartile range, and five number summary for the data on life expectancies below: 64, 72, 77, 64, 51, 81, 79, 77, 76, 71, 68, 48, 80, 71, 76, 69, 75, 74, 79, 67. Round to two decimal places

Mean=70.95 Standard deviation=8.92 Median=73.00 IQR=9.75 Five number summary: 48.00, 67.50, 73.00, 77.00, 81.00

Refer to the data set of body temperatures in degrees F and given in the accompanying table and use software or a calculator to find mean and median. Do the results support the common belief that the mean body temperature is 98.6? 98.9,96.9,99.0,96.8,96.9,97.7,99.0,98.0,99.2,97.3,97.0,97.7,99.1,99.0,97.2,99.0,96.7,97.7,99.2,99.2,97.5,99.1,97.1,97.4,98.1,98.4,98.8,96.8,97.3,98.3,97.3,97.7,98.1,98.5,97.0,99.5,98.6,99.6,99.0,99.1,99.2,97.8,98.7,98.7,99.5,97.6,98.2,97.5.

Mean=98.16 Median=98.1500 The results contradict the belief because both are less than 98.6 degrees F

What are nonresistant measures?

Measure that is influenced by outliers

What is mode?

Measurement that occurs most often

What is the response variable?

Measures of an outcome of a study

What does M mean (other than molarity)?

Median

What is the median?

Middle value when measurements are arranged from lowest to highest

Find the midrange and range for the number of tornadoes recorded each month in 2013: 75, 39, 18, 86, 265, 122, 71, 45, 21, 57, 78, 14

Midrange: 139.5 Range: 251

What is the x-bar approximately?

N( mean, standard deviation/ square root of the sample size)

Does the table below represent a correct probability distribution. If not explain why not x=P(x) 0=-0.05 1=0.05 2=0.15 5=0.25 10=0.60

No, not every probability is between zero and one

Does the table below represent a correct probability distribution. If not explain why not x=P(x) 0=0.05 1=0.05 2=0.15 5=0.25 10=0.60

No, the sum of the probabilities does not equal one

To determine the average life span of poodles, 15 female and 15 male poodles are randomly selected and their life span is recorded and compared between groups. Observational study or experiment?

Observational study

What are resistant measures?

Ones that can resist the influence of outliers

In modified box plots, a data value is a(n) _____ if it is above quartile 3 + (1.5)(IQR) or below quartile - (1.5)(IQR)

Outlier

The percent of women in the US over 18 who currently smoke is 16.5%. Parameter or statistic?

Parameter

What is a sample?

Part of the population from which we actually collect information

Which measure of variation is most sensitive to extreme values?

Range

What is a simple random sample?

Selected from the population in such a way that every simple random sample of n units has an equal chance of being selected. Works well when the units are homogenous with respect to the variable of interest

What is the range?

the difference between the highest and lowest scores in a distribution

What is a population?

the entire group of people you want to study

What is the population distribution?

The distribution of values of the variable among all the individuals in the population

What requirements are necessary for a normally probability distribution to be a standard normal probability distribution?

The mean is 0 and the standard deviation is 1

What is the median of a density curve?

the equal-areas point, the point that divides the area under the curve in half

Identify which of these designs is most appropriate for the given experiment. Completely randomized design, randomized block design or matched pairs design. Currently, there is no approved vaccine for the prevention of infection be a certain virus. A clinical trial of a possible vaccine is being planned to include subjects treated with the vaccine while other subjects are given a placebo.

The most appropriate is completely randomized design

To determine how the weight of a vehicle impacts the gas mileage, Ann randomly select 10 compact cars, 10 midsized cars, 10 SUVS, 10 vans and 10 trucks and records the weight in pounds and the gas mileage in miles per gallon for each of the vehicles. The response or dependent variable is

the gas mileage

Which of the following is not a requirement for constructing a confidence interval for estimating the population proportion?

The trials are done without replacement

What is randomized block design?

The units are first divided up based on prior information and random assignment is done separately within the groups. It is a lot like stratified random sample

What is a class midpoint?

The value in the middle of the class

To determine how the weight of a vehicle impacts the gas mileage, Ann randomly select 10 compact cars, 10 midsized cars, 10 SUVS, 10 vans and 10 trucks and records the weight in pounds and the gas mileage in miles per gallon for each of the vehicles. The explanatory or independent variable is

The weight of the vehicles

Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and diary products in our diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.

There does appear to be a potential for bias. They have an incentive to produce results that please the foundation funding them

One of Mendel's famous genetic experiments yielded 428 green and 154 yellow peas. Find a 90% confidence interval for the proportion of green peas and state the confidence interval in words. Give the final answer to 2 decimal places

There is 90% confidence that the interval (0.71,0.77) captures the population proportion of green peas yielded

it was found that 3200 of them used at least one prescription mediation. Construct a 90% confidence interval estimate of the proportion of adults aged 57-85 years who use at least one prescription medication. State confidence interval in words

There is 90% confidence that the population proportion is captured by the interval (0.7896, 0.8104)

A random sample of 25 flea beetles was taken and the mean for the maximal width of aedeagus in the forepart (in microns) was 134.81 microns with a standard deviation of 10.35 microns, find a 99% confidence interval for the mean maximal width of aedeagus in the forepart for all flea beetles.

There is 99% confidence that the interval (129.02, 140.60) captures the population mean maximal width of aedeagus in the forepart for all flea beetles population

A random sample of 30 breakfast cereals was taken and it was found that they contained on average 6.1 grams of sugar with standard deviation of 3.97 grams. Find a 99% confidence interval for the average amount of sugar found in breakfast cereal

There is 99% confidence that the interval (4.10, 8.10) captures the population mean for the average grams of sugar found in a serving of breakfast cereal

To estimate the average body temperature for adults, a random sample of 30 adults is selected and a mean body temperature of 98.20 degrees F and a standard deviation of 0.62 degrees F are calculated. Find a 99% confidence interval to estimate the mean body temperature of adults. State the confidence interval in words

There is 99% confidence that the population mean body temperature is captured by the interval (97.89, 98.51).

Lesotho is a mountainous country surrounded by South Africa. Because of the terrible soil erosion problems the country is facing, no till farming practices are being promoted. A random sample of 200 Lesotho farmers is selected and it is found that 95 of them are using no till farming. Find a 95% confidence interval for the proportion of Lesotho farmers using no till farming.

There is a 95% confidence that the interval (0.406, 0.544) captures the population proportion of Lesotho farmers who use no till farming

What is a binomial probability distribution?

the number of successes occurring in "n" trials, given the probability "p" of successes for each individual trial

Determine whether the study is an experiment or observation study, and then identify a major problem with the study. A sociologist has created a brief survey to be given to 2000 adults, randomly selected from the US population. Here are her first two questions (1) Have you ever been a victim of a felony crime? (2) Have you ever been convicted of a felony?

This is an observational study because the researcher does not attempt to modify the individuals. The problem is that those that have been convicted of a felony are more likely to not answer the second question honestly

What is sampling variability?

This is the natural variation of sample and is unavoidable and expected in random sampling but in most cases this isn't an issue

Which of the following is not a requirement of the binomial probability distribution?

Trials must be dependent

John randomly selected 20 students from an incomplete list of students. This could what kind of bias?

Undercoverage

What is an experiment?

We are interested in the influence of one or more variables or factors on the response. We always apply treatment to units in order to manipulate them. The environment is also manipulated in some way. If it is carefully designed and potential lurking variables are accounted for and controlled, conclusions regarding casualty can be made

What is the central limit theorem?

When a sample size (n) is large enough, the distribution of the sample mean will be normally distributed regardless of the original distribution of x

What is confounding?

When many variables have an impact on another variable making it difficult to determine which one causes the greatest change

What is common response?

When one variable makes two other variable appear related

What is common response?

When one variable makes two other variables appear to be associated, we have common response

How does non sampling error occur?

When sample data is incorrectly collected, recorded or analyzed

What is nonrandom or convenience sampling?

Where the sample is selected haphazardly or non-scientifically

What is random or probability based sampling?

Where the sample is selected in such a way that each unit in the population has a nonzero chance of being chosen

Ten unique students from universities in the US were randomly chosen and whether or not they smoke was recorded. Is this a binomial probability distribution?

Yes

Are there any outliers in the body fat data? 5.1, 6.9, 7.5, 8.5, 10.9, 12.0, 12.6, 12.8, 19.0, 20.5, 20.5, 20.5, 20.6, 20.8, 21.7, 21.7, 22.4, 24.6, 27.8, 40.1

Yes, 40.1

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administrated to 90 randomly selected individuals, with the number of individuals responding responding favorably recorded

Yes, because the experiment satisfies all the criteria for a binomial experiment

Does the frequency distribution appear to have a normal​ distribution? Explain. Temperature (degrees F) and frequency 35-39: 1 40-44: 4 45-49: 6 50-54: 14 55-59: 6 60-64: 2 65-69: 1

Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency and the distribution is approximately symmetric

Refer to the accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with 5 classes. Begin with a lower class limit of 120.6 volts and use a class width of 0.2 volts. Does the result appear to have a normal distribution? Why or why not? Volts and frequency 120.6-120.7: 3 120.8-120.9: 6 121.0-121.1: 9 121.2-121.3: 6 121.4-121.5: 1

Yes, because the frequencies start low, reach a max, then become low again, and are roughly symmetric about the max frequency

What is a census?

the official count of a population

What is nonresponse bias?

bias that arises when actual respondents differ from those who refuse to participate in ways that affect the survey results

What is the round off rule?

carry the answer to one more decimal place than is present in the original set of values

Is median a measure of center of spread?

center

Is the mean a measure of center or spread?

center

The education level of a person will impact their future income, but other factors will also impact their future income such as the degree they obtain, their ability to get a good job ect. This is an example of

confounding

A _____ random variable has infinitely many values associated with measurements

continuous

A _____ random variable has either finite or a countable number of values

discrete

A researcher is interested in the effects of exercise on memory. She randomly assigned half a group of students to run up three times and the other half to rest for an equivalent amount of time. Each student was the asked to memorize a series of random digits. She compared the number of digits remembered for the two groups. This is an example of an

experiment

To determine whether music will help children at a daycare calm down, five of the teachers play music to their children and five don't. This is an example of an

experiment

If a statistic is unbiased, then the value of the statistic must be the same in all sample of equal size. True or false

false

If the number of observations is even the median

is the average of the two center observations

If the number of observations is odd the median

is the center observation

A study wanted to look at how education impacts a person's future income. The outcome was not as strong as they anticipated because the degree the person obtained had an impact on their income. The degree is an example of a

lurking variable

What is the range equation?

max-min

Which of the following is not a value in the 5 number summary?

mean

What is the boundaries formula outside of which is considered unusual?

mean - 2(standard deviation) mean + 2(standard deviation)

A value at the center or middle of a data set is a(n)

measure of center

What is the five number summary?

minimum, Q1, median, Q3, maximum

What is the mean formula for binomial distribution?

n * p

What is the variance formula for binomial distribution?

n * p * q

What is the binomial formula?

nCx (p)^x (1-p)^n-x

One of the jars in the sample broke when Anne was weighing them, so she was unable to get a measurement for that jar. This may have caused

nonresponse bias

A unimodal, symmetric distribution is considered

normal

What is a statistic?

numerical summary of a sample

What is nonresponse?

occurs when an individual chosen for the sample can't be contacted or refuses to participate

What is unimodal?

one peak

____ are sample values that lie very far away from the majority of the other sample values

outliers

What is the large sample confidence interval for a population proportion formula?

p̂ - z alpha/2 (square root of p̂qˆ/n) < p < p̂ + z alpha/2 (square root of p̂qˆ/n)

What is data?

recorded observations

What is the symbol for sample standard deviation?

s

What is the symbol for sample variance?

s2 (s squared)

The ____ is the best point estimate of the population mean

sample mean

The _____ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further

sample space

Is range a measure of center or spread?

spread

Is standard deviation a measure of center of spread?

spread

What is the formula for standard error?

square root of p̂qˆ/n

Which sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each subdivision?

stratified