CHLD-3301.793 Introductory Statistics WEEK 1-7
The Centers for Disease Control & Prevention in Maryland reports that the mean weight (in pounds) for adult males aged 20 years and over is µ = 195. Assume that this distribution is normal in shape and the standard deviation = 30. Find the z score for a man with a weight of 246 pounds (that is, for X = 246). Round to the nearest tenths place if a fraction. [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.2 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value.]
+1.7
For a population automobile drives in a medium-sized city (population about 100,000), the traffic police ticketed numerous drivers speeding in school zones during school hours. The drivers' ticketed speeds formed a normal distribution with a mean of µ = 35 (miles per hour) and ơ = 5. With these parameters, answer the associated question(s). What proportion (not percent) of the ticketed drivers were driving equal to or faster than 50 mph?
.0013
You have a sample of 110 students of which 75 are freshmen, 15 are sophomores, 10 are juniors, and 10 are seniors. You pick one student at random from the roster and he/she is a senior. What is the probability, p, of drawing a senior student? Round to the hundredths place if a fraction.
.09
You have one hundred students in an underwater basket weaving course: 70 are freshmen, 15 are sophomores, 10 are juniors, and 5 are seniors. You pick one student at random from the roster and he/she is a freshman. What is the probability, p, of drawing a freshman student? Round to either the nearest tenths or hundredths place if a fraction.
.70
When the null hypothesis is true, the mean of the sampling distribution of the difference [between sample means] will have value of ______________.
0
The scores below are the heights, in inches, of number of grandchildren that elderly adults in an assisted living home moved have. Scores: 66, 68, 65, 67, 69, 66, 68, 68, 70, 65, 65 For these data, calculate the standard deviation, . Round to the nearest tenths place if a fraction. The standard deviation is:
1.6 or 1.7
A research report summarizing the results from a two sample dependent t test study states: "The data show no significant difference between the two treatments, t (10) = 1.65, p > .05." Based on this summary report, you can conclude that a total of _____________ individuals participated in the research study.
11
A population distribution has = 80 and = 6. In this distribution, a z-score of z = +2.00 identifies a location ________________ in original units (X).
12 points above the mean
An experiment for which the a two sample independent t test will be employed uses one sample with N = 6 and a second sample with N = 10 to evaluate a new treatment. The t test for this experiment will have degrees of freedom equal to ___________.
14
A medical researcher is investigating the claim that the mean body temperature of 17 year old females is different from the norm of 98.6 degrees. Which of the following is an example of an appropriate alternate hypothesis?
17 year old female body temperature differs from the 98.6 degree norm
Midterm exam scores for a Biology I lab class of ten students are given below. These scores represent the percent of items correctly marked on the midterm. 87, 99, 75, 87, 94, 75, 35, 88, 87, 93 For these data, calculate the standard deviation, ơ. Round to the nearest tenths place if a fraction. The standard deviation is:
17.2
The total number of pages in college textbooks has been found to be a normally shaped distribution with a mean of µ = 325 pages in length, and a standard deviation = 115. If you find that a particular textbook has a z score of z = -1.2, how many pages does it contain (that is, solve for X)? Round to the nearest tenths place if a fraction. [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.5 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value.]
187
A survey of 20 college students was conducted to determine how many fiction or nonfiction books they had read for pleasure during the past three months (not including books for school). The answers from those 20 students are below. 2, 4, 5, 1, 3, 2, 5, 6, 1, 2, 4, 3, 6, 10, 12, 10, 2, 8, 6, 7 For these data, calculate the mode. Round to the nearest hundredths place if a fraction. The mode is:
2
The scores below are the number of times that adults moved residences before completing high school (or, how many times they moved). Scores: 5, 5, 1, 3, 7, 5, 4, 6, 2, 8, 6, 7, 3 For these data, calculate the standard deviation, . Round to the nearest tenths place if a fraction. The standard deviation is:
2
The scores below are the number of cups of coffee one Google employee drank per day in a 7-day week. The number of cups a Google employee consumed per day for seven days: 5, 4, 8, 5, 9, 2, 4 For these data, calculate the standard deviation, ơ. Round to the nearest tenths place if a fraction. The standard deviation is:
2.2
The scores below are the heights, in inches, of number of grandchildren that elderly adults in an assisted living home moved have. Scores: 66, 68, 65, 67, 69, 66, 68, 68, 70, 65, 65 For these data, calculate the population variance, . Round to the nearest tenths place if a fraction. The variance is:
2.7
Blood pressure is measured in millimeters of mercury (mm Hg) and recorded with the systolic number first, followed by the diastolic number. The normal mean systolic blood pressure of female college students is µ = 120 mm Hg. You are a physiological psychologist and prior studies indicate that as anxiety increases, systolic blood pressure increases. You predict that taking tests, especially statistics tests, arouses anxiety, and hence systolic blood pressure will increase when taking statistics tests. Twelve college females enrolled in statistics volunteer to have their systolic blood pressure measured midway through their first statistics test. Their mid-test blood pressures are presented below. 118, 133, 142, 132, 111, 140, 122, 149, 124, 116, 128, 129 With alpha equal to α = .01, determine the critical value of z* or t* that needs to be employed here. The value of the appropriate of z* or t* is:
2.718
Assume you're interested in the mental health effects of the "caregivers" caring for the elderly with Alzheimer's disease. Specifically, you expect that such caregivers will suffer from significantly elevated levels of depression as compared to the general population. To measure depression in care-givers, you use a standard test of depression (STD) on which scores range from zero to 40, with high scores indicating higher levels of clinical depression. The mean in the general (normal) population of on this test is µ = 20. You get permission from ten caregivers who have worked in a local assisted living facility for Alzheimer's patients for over two years to participate in your study. They are administered the STD and their scores are below. 18, 33, 32, 22, 31, 29, 21, 26, 17, 25 Set your alpha level at α = .01. Complete step 3 of the hypothesis testing procedure and calculate z or t, whichever is appropriate for these data. Round to the nearest hundredths place. If your calculated z or t is not identical to one of the values below, but within plus or minus 0.2 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value. Ignore the minus sign if your calculated z or t is negative
2.95
A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score, the z-score would be _______________.
3
In the frequency distribution where X refers to quiz scores (the number correct), how many individuals took the quiz? X F 15 12 14 11 13 5 12 0 11 2
30
For a population automobile drives in a medium-sized city (population about 100,000), the traffic police ticketed numerous drivers speeding in school zones during school hours. The drivers' ticketed speeds formed a normal distribution with a mean of µ = 35 (miles per hour) and ơ = 5. With these parameters, answer the associated question(s). What is the speed someone was driving where 40 percent of the ticketed drivers were driving at or below this speed? Round to the nearest tenths place if a fraction.
33.75
A researcher believes that a common over-the-counter medication for arthritis, Advil, will have a negative effect on driving ability when administered in high doses. You ask a group of seven adults who have arthritis and use Advil to participate in a driver simulation task while under the influence of a high amount of Advil. You record the following braking times (in seconds) required to stop upon seeing a car stopped ini the same lane in front of them. You expect the Advil drivers to have significantly retarted or slower (hence longer braking times, or increased braking times) braking times than the normative group. The mean braking time on this task for persons with arthritis who have not self-administered Advil or other drugs is μ = 0.7 seconds. Remember, higher braking time scores mean that the individual is "slow", and the researcher expects Advil will slow braking times. Braking times (in seconds) 1.2 1.0 1.1 1.4 0.9 1.0 1.6 Complete step 3 of the hypothesis testing procedure and calculate z or t, whichever is appropriate for these data. Round to the nearest hundredths place. If your calculated z or t is not identical to one of the values below, but within plus or minus 0.2 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value. Ignore the minus sign if your calculated z or t is negative.
4.99
Scores on Part 1 of the statistics quiz for each of nine students are: Scores: 0, 4, 6, 5, 9, 9, 7, 6, 2 Calculate the raw score corresponding to the 40th percentile. Round to the nearest tenths place if a fraction. The raw score is: [deleted]
5
The scores below are the numbers of dogs that nine "dog-loving" families have: Dogs in the family: 5, 7, 8, 6, 4, 3, 2, 6, 5 For these data, calculate the mode.
5&6
The scores below are the number of cups of coffee one Google employee drank per day in a 7-day week. The number of cups a Google employee consumed per day for seven days: 5, 4, 8, 5, 9, 2, 4 For these data, calculate the population variance, ơ2. Round to the nearest tenths place if a fraction. The variance is:
5.1
The mean birth weight for full-term newborns in the USA is µ = 7.5 pounds. Assume that this distribution is normal in shape and the standard deviation = 2.0. Low birth weight is defined as a weight less than a z score of z = -1.0. What is the birth weight, in pounds, that defines a full-term newborn as a "low birth weight"baby (that is, solve for X)? Round to the nearest tenths place if a fraction. [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.5 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value.]
5.5
The shape of a given distribution is normal with a mean of 450 and a standard deviation of 60. With these parameters, answer the associated question(s). For these parameters, calculate the raw score (X) corresponding to a z score of z = 1.65. Round to the nearest tenths place if a fraction. The X score is:
549
Scores on Part 1 of the statistics quiz for each of nine students are: Scores: 0, 4, 6, 5, 9, 9, 7, 6, 2 Calculate the percentile rank for a raw score of 6. Round to the nearest tenths place if a fraction. The percentile rank is:
66.7
The scores below are the number of students who call in sick to a local elementary school during flu season, each day for one week, beginning Monday through Friday. Number of student absences on a particular day of the week: 24, 18, 11, 13, 31 For these data, calculate the standard deviation, ơ. Round to the nearest tenths place if a fraction. The standard deviation is:
7.3
The total number of pages in college textbooks has been found to be a normally shaped distribution with a mean of µ = 325 pages in length, and a standard deviation = 115. . Find the percentage of books that have equal to or more than 500 pages in length. Round to the nearest hundredths place if a fraction. [Note, if your calculated value is not identical to one of the values below, but within plus or minus 0.25 of an answer below, assume it's a rounding error and select the answer that is closest to your calculated value.]
7.95
The scores below are a sample of scores of the statistics final exam that N = 12 students made. Final exam sample scores: 92, 81, 96, 94, 53, 24, 61, 73, 100, 71, 92, 20 For these data, calculate the sample mean, M. Round to the nearest tenths place if a fraction. The mean is:
71.4
The scores below are "college readiness" scores of 15 graduating high school seniors, with higher scores indicating an individual is more ready for college in terms of social/academic preparedness than low scores. The highest score possible is 100. 90, 94, 53, 68, 79, 84, 87, 72, 70, 69, 65, 89, 85, 83, 72 Using the percentile rank formula, Formula 1 on page 2 of Week 3 book content, calculate the percentile rank that corresponds to a score of 87. Round to the nearest tenths place if a fraction. The percentile rank of X = 87 is:
80.0
Last week Tom had exams in Statistics and in English. He scored 10 points above the mean on both exams. From this information, what can you conclude?
Both of Tom's z-scores are positive
In a two-sample ______________design, either the same subjects (participants) are tested in one condition and then retested in the other condition, or the subjects in one condition are equated or matched with a specific subject in the other condition.
Dependent
You believe that eating 5 pixie sticks in a row will increase a 10-year old's hyperactivity behavior within 30 minutes after consumption. Which of the following is an example of an appropriate alternate hypothesis?
Eating 5 pixie sticks increases hyperactivity levels in ten-year-old children.
If the probability of Event A occurring is p = .09 and the probability of Event B occurring is p = .05, then which event is more likely to occur?
Event A
A Type II error (or beta error) is defined as ________________.
Failing to reject a false null hypothesis
Lowering the alpha level from .05 to .01 will increase the power of a statistical test.
False
Men's t-shirt sizes are classified as small, medium, large, extra large, and double extra large. This is an example of measurement on a nominal scale.
False
The mean is considered to be the "midpoint" for a distribution because exactly half of the scores are located above the mean and exactly half are below the mean.
False
With a two-tailed hypothesis test, HA is that the mean from which your sample was drawn is equal to one specific value.
False
A researcher knows that the weights of 3-year old children are normally distributed with µ = 40 pounds and ơ = 8. She speculates that children in poverty-stricken regions are undernourished and therefore underweight. With a sample of N = 12 children in a poverty-stricken zone of a large metropolitan city, the researcher obtained the weights of each child. Determine if the weights for this sample are significantly lower than what would be expected for the regular population of 3-year-olds. The weights (in pounds) for this sample are: 48, 45, 42, 37, 29, 33, 35, 39, 24, 32, 40, 42 Which of the following are the correct statements of the null and alternate hypotheses, H0 and HA ?
H0: µ 40 and HA: µ < 40
Blood pressure is measured in millimeters of mercury (mm Hg) and recorded with the systolic number first, followed by the diastolic number. The normal mean systolic blood pressure of female college students is µ = 120 mm Hg. You are a physiological psychologist and prior studies indicate that as anxiety increases, systolic blood pressure increases. You predict that taking tests, especially statistics tests, arouses anxiety, and hence systolic blood pressure will increase when taking statistics tests. Twelve college females enrolled in statistics volunteer to have their systolic blood pressure measured midway through their first statistics test. Their mid-test blood pressures are presented below. 118, 133, 142, 132, 111, 140, 122, 149, 124, 116, 128, 129 Which of the following are the correct statements of the null and alternate hypotheses?
H0: µ ≤ 120 and HA: µ > 120
A sleep researcher hypothesizes that college students who are deprived of sleep will perform significantly lower on tests of cognitive ability than the general student body who likely slept around eight hours. One standardized test of cognitive ability, called the STCA, reveals that mean score for college students who slept around eight hours is µ = 4.5. Scores on the STCA range from 1-9 with high scores indicating better performance. The researcher brings 15 volunteer participants into the sleep lab one night and limits their sleep to four hours. The next morning he administers the STCA. Their scores are below. 2, 3, 3, 2, 5, 3, 3, 3, 6, 7, 2, 5, 4, 3, 4 Which of the following are the correct statements of the null and alternate hypotheses?
H0: µ ≥ 4.5 and HA: µ < 4.5
A teacher gave a reading test to a class of 5th-grade students and computed the mean, median, and mode for the test scores. Which of the following statements is the only accurate description of the scores that can be made?
Half of the students had scores equal to or above the median
A worker at your local health food store tells you that research shows that large doses of vitamin C helps prevent the common cold. You decide you're going to test this claim. Which of the following is an example of an appropriate alternate hypothesis?
Large doses of vitamin C reduces the chance of catching a cold
The ____________ is most useful for nominal data, whereas the median is more useful with ____________ data.
Mode, Skewed
After measuring a sample of individuals, a researcher finds that one participant's score is bigger than another participant's score, but the researcher can't specify how much bigger. The measurements must come from a(n) ____ scale.
Ordinal
Rating a group of large metropolitan cities in the USA in terms of "quality of life" using ratings of 1, 2, 3, 4, and 5, with "1" reflecting the lowest quality and "5" reflecting the highest quality, would be an example of measurement on a(n) ____________ scale of measurement.
Ordinal
Which of the following is true for a normal distribution?
The mean, median and mode are all equal
In general, what is the relationship between the standard deviation and variance?
The standard deviation is the square root of the variance
A positive z-score always corresponds to a score greater than the mean.
True
Changing the level alpha from .01 to .05 increases the risk of a Type I error (or alpha error).
True
If a set of exam scores forms a negatively skewed distribution, it suggests that the majority of the students scored well on the exam (where higher scores indicate better performance).
True
If the highest score in a distribution is X = 12 and the lowest score is X = 4, then the range is 9 points.
True
The major advantage of constructing a frequency polygon instead of a histogram is that two or more distributions may be easily depicted on the same set of axes when you use the polygon rather than bars.
True
The tools of descriptive statistics enable one to simplify, summarize, and organize data.
True
Within any distribution of scores, the location specified by z = +1 and the location specified by z = -1 are exactly the same distance from the mean.
True
A researcher measures persons "Social Status" in terms of low, moderate and high levels. Here, "Social Status" is an example of a(n)
Variable
What value is obtained if you add all the deviations from the mean for a population, then divide the sum by N?
You will always get zero
For a two-tailed test with = .05, you should reject H0 if the ____________ of the calculated z score (or calculated t score) is greater than the critical value of z (or t)
absolute value
The hypothesis testing procedure consists of a series of steps to help you decide which one of two competing hypotheses is more likely correct. One of these hypotheses is called the null hypothesis and the second is called the ___________________ hypothesis.
alternate
A researcher risks a Type I error (or alpha error) ________________.
anytime Ho is rejected
A Type II error (or beta error) means that a researcher has ______________.
concluded that a treatment has no effect when it really does
The class of statistical techniques that summarize, organize, and simplify data are classified as ____________.
descriptive statistics
If one actually selected many samples from a population and calculated the sample means, the resulting sampling distribution is referred to as a(n) __________ sampling distribution
empirical
If the obtained sample mean falls in the region of rejection, then your decision in Step 4 of the hypothesis testing process should be to retain H0.
false
If the same subjects participate in both conditions of a particular two-sample research design, then the two-sample independent t test should be employed.
false
Using a two-tailed test, with your level of alpha and df, if the value of your calculated t is greater in absolute magnitude than t*, you can reject HA.
false
For the past 20 years, the high temperature on April 15th has averaged = 92 degrees with a standard deviation of = 4. But on the recent April 15 date, the 21st year, the high temperature was 102 degrees. Based on this information, the recent year's temperature on April 15th was _______________
far above average
What is meant by________ samples is that the subjects cannot be paired up or matched in any way.
independent
Since extreme values in a distribution do not affect the median, the __________ is preferred with interval/ratio data when the data are extremely skewed.
median
A researcher measures personality for a sample of n = 50 people and classifies each person as either Type A, Type B, or Type C personality. Which measure of central tendency would be appropriate to summarize these measurements?
mode
As a nutritionist, your experience has lead you to predict that persons defined as obese consume more carbonated beverages (soft drinks, soda, pop) per week than the general population. Is this a one-tailed HA or a two-tailed HA ?
one tailed
Assume you're interested in the mental health effects of the "caregivers" caring for the elderly with Alzheimer's disease. Specifically, you expect that such caregivers will suffer from significantly elevated levels of depression as compared to the general population. To measure depression in care-givers, you use a standard test of depression (STD) on which scores range from zero to 40, with high scores indicating higher levels of clinical depression. The mean in the general (normal) population of on this test is µ = 20. You get permission from ten caregivers who have worked in a local assisted living facility for Alzheimer's patients for over two years to participate in your study. They are administered the STD and their scores are below. 18, 33, 32, 22, 31, 29, 21, 26, 17, 25 Is this a one-tailed HA or a two-tailed HA ?
one tailed
You have a jar with ten gumballs. Five are red, three are white, and two are green. You pick two gumballs in a row. After picking the first gumball you place it back into the jar and then select your second gumball. What is the probability, p, of drawing a white and then a green gumball? Round to the nearest hundredths place if a fraction.
p=.06
You have a face-to-face statistics class in the traditional classroom setting. There are 25 males and 45 females enrolled. You're the instructor so you like to arrive in the classroom before the first students arrive. What is the probability that the first student who arrives is a male? Round to the nearest tenth or hundredths place.
p=36
When you say that 70% of the scores were less than or equal to a particular raw score, it follows that the raw score has a(n)_______________ of 70.
percentile rank
A researcher is interested in the average of time that 9th grade boys in the United States spend playing video games. The entire group of 9th grade male students in the U.S.A. is an example of a _________.
population
Before applying the dependent t test, if you have matched pairs of different subjects, it is necessary to assume that the subjects in each pair are ____________ assigned to one or the other of the two groups.
randomly
The power of a statistical test is the probability of _________________.
rejecting a false null hypothesis
A researcher administers a treatment to a sample of n = 25 participants and uses the z test to evaluate the effect of the treatment. The hypothesis test produces a calculated z = 2.37. The critical value of z* is 2.58 for a two tailed test with = .01. What is the appropriate decision to be made in Step 4 of the hypothesis testing procedure?
retain Ho
An athletic coach is interested in the effects of smoking cigarettes on physical endurance. Which of the following is an example of an appropriate alternate hypothesis?
smoking affects endurance
The standard deviation is closely related to the variance. In fact, the standard deviation is the ____________ of the variance.
square root
When a person has a z score of 1.8, for example, it means that the person's raw score (X) equivalent is 1.8 _________________ units above the mean.
standard deviation
The standard deviation of the sampling distribution of the difference [between sample means] is also referred to as the _____________ of the difference.
standard error
Eight White adults had been convicted of crimes of hate for their anti-Asian behaviors and were asked to participate in treatment as part of their probated court sentences. Part of the treatment package consisted of watching a movie designed to increase tolerance and appreciation of cultural diversity. A "Diversity Attitude Checklist" (DAC) was completed by each participant before and after watching the movie. Using the pre and post movie DAC scores below, test the researcher's hypothesis that the movie will result in an increase in tolerance and appreciation for cultural diversity attitude (raise DAC scores). High scores on the "Diversity Attitude Checklist" indicate more tolerance and appreciation. Participant Pre-Movie DAC Score After Movie DAC Score A 28 36 B 25 25 C 27 26 D 29 31 E 25 28 F 21 22 G 27 33 H 25 29 With = .05, summarize the results of the hypothesis testing procedure by putting your results in journal form. Ignore the minus sign if your calculated t is negative.
t (7) = 2.67, p < .05
The numerator of the z test formula measures ________________.
the actual difference between M and u
The sampling distribution of the mean (or sampling distribution for short) consists of a distribution of ____________.
the means of many equal sized samples drawn from the population
When untreated during their lifetimes, a certain strain of cancer susceptible rats has an average lifespan of 134 days. To determine the effects of a new potentially cancer-retarding drug, a new study is being conducted. In this study, which of the following is an example of an appropriate alternate hypothesis?
the new drug will increase the lifespan of rats
The results of a two sample independent t test are reported as, t (5) = 2.12, p > .05, for a two tailed test. What statistical decision was made in step 4 of the hypothesis testing procedure?
the research retained Ho
According to the Central Limit Theorem, the value of the mean of the sampling distribution of the mean is the population mean, µ.
true
The population mean always corresponds to a z-score of zero.
true
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis, H0?
u less than or equal to eighty
A population is known to have a mean of = 50. A treatment is expected to decrease scores for individuals in this population. The treatment effect will be evaluated using a one-tailed hypothesis test. Which of the following is the correct statement of the alternate hypothesis, HA?
u<50
A study in which the two sample independent t test should be applied ______________
uses a different sample of subjects for each of the two treatment conditions being compared
You have 30 marbles, five are blue, seven are red, three are white, and 15 are green. You pick one marble at random. Which color of marble has the lowest likelihood of being picked on that single draw?
white
An administrator in charge of undergraduate education at UT Permian Basin wanted to know whether the number of books that professors require of students per course has changed in Spring semester as compared to the previous Spring semester a year ago. The administrator knows that a year ago in Spring the mean number of books that instructors required per course was normally distributed with μ = 2.2 and σ = 0.6. With a sample of N = 15 classes this current Spring semester, the administrator obtained the following number of books that a professor required per class: 1, 3, 0, 2, 1, 5, 4, 2, 2, 7, 1, 1, 2, 2, 3 Set your alpha level at = .01, and summarize the results of the hypothesis testing procedure by putting your results in journal form. Ignore the minus sign if your calculated z or t is negative.
z = 1.29, p > .01
An administrator in charge of undergraduate education at UT Permian Basin wanted to know whether the number of books that professors require of students per course has changed in Spring semester as compared to the previous Spring semester a year ago. The administrator knows that a year ago in Spring the mean number of books that instructors required per course was normally distributed with µ = 2.2 and σ = 0.6. With a sample of N = 15 classes this current Spring semester, the administrator obtained the following number of books that a professor required per class: 1, 3, 0, 2, 1, 5, 4, 2, 2, 7, 1, 1, 2, 2, 3 Which hypothesis test needs to be employed here, the z test or the one-sample t test?
z test
For a distribution of scores, which of the following z-score values represents the location closest to the mean?
z=+0.50
