STAT Final Exam- Test questions Review

A survey was administered that asks the following questions. 1. In what setting did you grow up? Rural Suburban City Other 2. Do you plan to raise your kids in the same setting? Yes No To perform a chi-square test of association between these two variables, Which is the correct language for null and alternative hypotheses?

( if more than 2 categories you write it out) but Ho: p1 = p2 = p3 Ha: at least one p(i) differs

Researchers are interested in determining whether there is a relationship between political party and whether or not a person supports additional funding for special education in schools. After performing a chi-square test for association, the chi-square statistic is calculated to be 2.86 with a p-value of 0.4137. The picture of the p-value is below. picture x axis= 2.86 red coloring is 0.4137

) The probability of getting a chi-square statistic of 2.86 or any value larger, assuming the null hypothesis is true, is 0.4137.

You are provided with the following information from a Minitab regression output. The regression equation is y = 3 - 0.5x. The squared correlation is 81%. Find the correlation coefficient.

-0.9

In the process of conducting a 2-sample z-test for the difference of two population proportions we calculate that p-hat(1) = 0.12 and p-hat(2) = 0.16. The standard of the difference is s.e.(p-hat(1) - p-hat(2)) = 0.02. What is the test statistic to test the hypotheses below? Ho: p1 - p2 = 0 Ha: p1 - p2 < 0

-2

A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation: y = 11 + 0.25x One student in the sample was 70 inches tall with a foot length of 26.5 cm. What is the residual for this student?

-2.00

A researcher is testing the hypotheses below: Ho: mu = 150 Ha: mu < 150 After summarizing a dataset of size n=25, the sample estimate is x-bar=147 with a standard deviation of 5 What is the test statistic?

-3

Find the standard dev of set of numbers : 6, 6, 6, 6, 6

0

It is known that 30% of a certain company's washing machines require service while under warranty, whereas only 10% of its dryers require such service. If someone purchases both a washer and a dryer made by this company, what is the probability that both machines need warranty service? Assume that the two machines function independently of one another.

0.03

Two researchers Donna and Eileen each select random samples of size 1000 from different populations and construct 95% confidence intervals. The half-width of Donna's interval is .030 and the half-width of Eileen's is .025. Given that the sample proportions were .20 and .40, what was Eileen's sample proportion?

0.20

A distribution of measurements is bell-shaped with mean 50 and standard deviation 10. About what proportion of measurements will fall between 50 and 60?

0.34

Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the event that the selected individual has a MasterCard credit card. Suppose that P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.25. What is the probability that the selected individual has neither type of card?

0.35

Find the mean and the standard deviation of the sampling distribution of possible sample proportions for a sample size of n = 400 with population proportion p = 0.5.

0.5 and 0.025 respectively

yes no total 18-29/ 25 ----- 215 ------240 30 + / 46------214-------260 total 71------439-------500 Relative Risk of seeing a ghost for adults under 30 compared to adults 30 and over

0.589

Suppose that the resting breathing rates for college-age students have a distribution that is bell-shaped, with a mean of 12 and standard deviation of 2.3. What proportion of all students would have breathing rates in the interval from 9.7 to 14.3.

0.68

0 1 2 3 4 .10 .20 .50 .15 0.05 What is the probability that at least 1 student comes to office hours on Wednesday?

0.90

Suppose the true (population) proportion of adults who approve of the job the president is doing is 55%. A newspaper conducts a poll to determine the proportion of adults who say they approve of the president's work. They ask a random sample of 200 adults whether or not they approve. What is the probability that the newspaper would have recorded a sample proportion between 48% and 62%? You are also given that the standard error of the sample proportion is 0.035.

0.95

In a certain residential suburb, 60% of all households subscribe to the metropolitan newspaper published in a nearby city, 80% subscribe to the local paper, and 50% of all households subscribe to both papers. If a household is selected at random, what is the probability that it subscribes to at least one of the two newspapers. A) 0.90 B) 0.10 C) 0.50 D) 0.80 E) 1.00

1. 0.90

Which of the following statements is false? A) The number of overdue accounts in a department store at a particular time is a continuous random variable. B) Number of defects on a randomly selected piece of furniture is a discrete random variable. C) The tensile breaking strength (measured in pounds per square inch) of a 1-inch-diameter steel cable is a continuous random variable.

1. the number of overdue accounts in a department store at a particular time in a continuois random variable

z mult for a 70 % confidence interval

1.04

yes no total men 35 165 200 women 45 255 300 Relative risk of suffering from sleep apnea for men compared to women is

1.167

0 1 2 3 .10 .40 .30 .20 Find the expected value, average number of times a customer visits the store

1.60

The mean duration of television commercials on a given network is approximately bell-shaped with a mean of 75 seconds and standard deviation of 20 seconds. What is the duration of a commercial that has a z score of 1.50?

105

To determine if the average German shepherd show dog weighs more than 80 pounds, you visit a dog show and weigh 15 German Shepherds. You calculate a test statistic of 1.29. How many degrees of freedom does this t-statistic have?

14

Male Female pre k 8 9 no 6 2 what is the the prob that the students is either female or went to prek?

19/25

How many of the factors below influence the width of the confidence interval for one population proportion? Sample size, n sample proportion, p-hat population size

2

To test the hypotheses Ho: p=.4 Ha: p not equal .4 We take a random sample of 160 people and calculate a p-hat of 0.48. What is the z-statistic for this p-hat?

2.07

**** You are given the sample variance of a data set is 5.70. Find the standard deviation

2.39

A distribution of measurements is bell shaped with a mean of 50 and SD of 10. ABout what percentage of measurements will be greater than 70?

2.5

The mean duration of television commercials on a given network is approximately bell-shaped with a mean of 75 seconds and standard deviation of 20 seconds. What is the duration of a commercial that has a z score of -2.5?

25

A company that manufactures coffee for use in commercial machines monitors the caffeine content in its coffee. Suppose the company constructs 720 confidence intervals for the mean caffeine content μ in a month. If the level of confidence is 95% for all 720 confidence intervals, how many of the confidence intervals would you expect to fail to contain μ? A) 720 B) 95 C) 36 D) 684 E) none

36

A study is conducted comparing a student's height versus the height of their father. The correlation between father's heights and student's heights for 79 male students was r = 0.72. What is the proportion of variation in son's heights explained by the linear relationship with father's heights?

51.84 (not the +/-)

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law that requires all automobile passengers to wear a seat belt. What would be the approximate margin of error if the researcher randomly sampled 240 adults?

6.45%

Suppose that a conservative 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 68% plus or minus 4%. Find the sample size, n, that was used to obtain this confidence interval.

625

The percent of data which lie between the minimum and the upper quartile is

75%

The regression equation was found to be y = 3.00 + 0.475x. In this equation, y stands for number of errors, and x stands for number of hours without sleep. The predicted number of errors for a person who has gone 12 hours without sleep is

8.70

A 95% confidence interval constructed using a sample proportion and conservative margin of error indicates that

95% of the intervals constructed using this process based on samples from this population will include the population proportion

Which of the below formulas is never a valid formula for a test statistic? A) p hat- 0.5/n B) d bar -0 /sd / sq rt n C) (sample estimate - null value) / (standard error) D) x bar -mu/ s/sq rt n

A p-hat- 0.5 ------------ n

___ of only a few thousands, or perhaps even a few hundred, can give reasonable accurate information about a population of many millions

A representative sample

A researcher is interested in the mean difference in height for the male and female in fraternal twin pairs in which there is one of each sex. Which of the following statements is true? A) The explanatory variable is sex B) The explanatory variable is Height C) This is a randomized experiment D) The response variable is sex

A. explanatory variable is sex

In which of the following situations is the value given in bold a parameter? A) In the year 2000 census, the U.S. Census Bureau found that the median age of all American citizens was about 35 years B) The mean hours of study per week was 15 hours for a sample of n = 30 students at a college. C) For a sample of 20 men and 25 women, there is a 14 cm difference in the mean heights of the men and women. D) A polling organization samples 1000 adults nationwide and finds that 72% of those sampled favor tougher penalties for persons convicted of drunk driving.

A. in the year 2000 census, the US Census Bureau found that the median age of all American citizens was about 35

Which statement is true about a 90% confidence interval? A) A general expression for computing a 90% confidence interval based on data is sample estimate ± standard error. B) If we consider all possible randomly selected samples of the same size from a population, the percentage of those samples for which the confidence interval includes the population parameter is 90. C) The probability that the true value of the population parameter falls between the bounds of an already computed confidence interval is roughly 0.90.

B. if we consider all possible randomly selected samples of the same size from a population, the percentage of those samples for which the confidence interval includes the population parameter is 90.

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January. Let B be the event that the household does not exceed the lifeline usage during July. Suppose P(A) = 0.80, P(B) = 0.7, and P(A and B) = 0.5. Which of the following statements is true? A) The events A and B are complementary and independent. B) The events A and B are neither mutually exclusive nor independent C) The events A and B are independent and mutually exclusive D) The events A and B are complementary and mutually exclusive

B. the events a and b are neither mutually exlusive nor independent

n 2013 a survey was conducted of over 1,000 cell phone users in the US. 60% of respondents said that they use their cell phones to access the internet, and the margin of error was 2.4%. Which of the statements below is FALSE, statistically speaking? A) More than half of Americans use their cell phones to access the internet. B) The confidence interval for the percent of all Americans who use their phones to access the internet is from (57.6% to 62.4%). C) If the population size was larger the margin of error would also be larger D) If the sample size had been larger the margin of error would have been smaller

C. If the population was larger the margin of error would also be larger

yes no drug 1 18 82 100 drug 2 9 91 100 which of the following is false? A) The odds of experiencing nausea for drug 1 18/82. B) The risk of experiencing nausea for drug 2 is 9/100. C) The risk of experiencing nausea for drug 1 is 18/200. D) The odds of experiencing nausea for drug 2 is 9/91

C. the risk of experiencing nausea for drug 1 is 18/200

A variable that is not the main concern of the study but may be partially responsible for the observed results is knows as

Confounding Variable

A school counselor is interested in estimating with 90% confidence the proportion of high school seniors who have applied to at least one college. What should he do?

Construct a 90% confidence interval for a single population proportion

Which of the below formulas is never a valid formula for a confidence interval? A) (sample estimate) +/- (margin of error) B) (sample estimate) +/- (multipler) x (Standard error) C) (sample estimate) +/- (multipler) x s/ sq rt n D) (sample estimate) +/- (margin of error)/ sq rt n

D

A regression equation was fit for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y). The latitude is measured in degrees and average January temperature in degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is y = 49.4 - 0.313x In order to avoid extrapolation, it would be inappropriate to use the regression line to make predictions for all of the following cities except A) Copenhagen (latitude 55 degrees) B) Aberdeen (latitude 57 degrees) C) Hong Kong (latitude 22 degrees) D) Detroit (latitude 42 degrees) E) Kingston (latitude 17 degrees)

D, Detroit (42)

Consider the following null and alternative hypotheses: H0: p = .65 versus Ha: p < .65. If the Z test statistic returned by Minitab is -1.45, what is the p-value? Hint: draw this p-value on the standard normal distribution, and then use the empirical rule to choose the best answer A) 0.9882 B) 0.0241 C) 0.9265 D) 0.0735

D. 0.0735

A test of the hypotheses H0: p = .25 versus Ha: p > .25 provides a p-value of 0.11.

Fail to reject the null hypothesis and conclude that there is insufficient evidence to claim that p>.25 in the population

Is your overall satisfaction with a hotel room correlated with the cost of the room? You are provided with the following regression equation based on data collected on room prices and customer satisfaction ratings: Rating = 4.55 - 0.25*Price. What is the correct interpretation of the slope?

For each one every unit increase in price there is a 0.25 unit decrease in average rating

A researcher took a random sample of high school seniors on the track team. Each student's time was recorded for a one-mile run. A week later, the same students were each told to drink two shots of espresso an hour before running the same course for the one-mile run. Again, their times were recorded. Researchers are interested in determining whether the mean difference between non-caffeinated and caffeinated running times differs from 0. Which set of null and alternative hypotheses should they test?

Ho: mu(difference) = 0 Ha: mu(difference) not equal 0

A reporter for the New York Times is researching a story on the job outcomes for college graduates. She finds a paper that claims 40% of graduates move back in with their parents within one year. She thinks that this number is too high and wants to show that the true percentage is lower. She surveys 400 individuals and finds that 30% of them reported moving back in with their parents. Which set of hypotheses should she test?

Ho: p = .4 Ha: p < .4

Steve, a candidate for Senate, says that 2/3 of all women work outside the home. Susan, his opponent, believes the percentage is different. She conducts a survey in order to find out. Susan randomly samples 506 women, and finds that 370 of them work outside the home. What are the correct null and alternative hypotheses for Susan to test in this situation?

Ho: p = 2/3 Ha: p not equal 2/3

A childhood development expert wants to determine whether children born in July are more likely to be diagnosed with ADHD than children born in September. She reviews records from a local elementary school and finds that 12% of the 115 children born in July have been diagnosed with ADHD compared with 10% of the 130 students born in September. What hypotheses should she test in order to answer her question?

Ho: p(July) - p(September) = 0 Ha: p(July) - p(September) > 0

Which two statistics give information only about the spread of a dataset and NOT the location

IQR and Standard Deviation

Which of the following is not a continuous variable? -a persons body temperature -number of claims received by an insurance company during one day -weight of two dozen shrimp -height in inches of freshman at your university

Number of claims received by an insurance company during one day

All of the following are categorical variables except -gender of a student -color of a car entering the parking lot -number of flowers on an azalea plant -the state in which a person lives in

Number of flower on an azalea plant

Suppose that the correlation between educational level attained and yearly income is +0.68. Thus we know that

People with lower educational levels tend to have lower incomes

The correlation coefficient between a skater's stride rate (number of strides per second) and the length of time to cover the 6-meter distance is -0.37. In the regression equation between length of time (response) and stride rate (explanatory variable), which of the following answer options provides the correct value of the squared correlation as well as it's interpretation?

R squared equals 13.69% and it represents the proportion of variation in length of time which is explained by stride rate.

Imagine an experiment done to compare two methods for increasing memorization skills. Age affects memorization ability, so the researchers choose to divide participants into three groups (young, middle-aged, elderly) and then randomly assign each of the two methods to half the individuals in each age group. Which of the terms below is the best for describing this experiment's design?

Randomized block design

An experiment will be done to determine whether college students learn information better when listening to rap music, when listening to classical music, or when not listening to music. In the study, each participant will be randomly assigned to rap, classical, or no music and then they will read chapter 2 from a history book before taking a test on the material. The next day they are randomly assigned one of the remaining music types before reading chapter 3 from the history book and then taking a test on the material. On the final day the participants listen to the last of the three music types while reading chapter 4 from the book and take a test on the material. Which of the terms below best describe the design of this experiment?

Repeated measures

Exams scores (in percentages) range from 0 to 100. Suppose an exam for STAT 200 was difficult and most of the students scored low with only a few students scoring high. Which would best describe the shape of the distribution

Right Skewed

What statistic is NOT resistant to an outlier in the data?

Standard Deviation

A study was conducted to determine the effects of sleep deprivation on people's ability to solve problems without sleep. The regression equation was found to be y = 3.00 + 0.475x. In this equation, y stands for number of errors, and x stands for number of hours without sleep. The correct interpretation of the y-intercept is

The average number of errors for a person who has gone 0 hours without sleep is 3.00

Say, for example, the correlation is 0.75 between fat content (measured in grams) and cholesterol level (measured in milligrams) for 20 different brands of American cheese slices. If cholesterol level were changed to being measured in grams (where 1 gram = 1000 milligrams), what effect would this have on the correlation?

The correlation would remain the same

Which of the following would indicate that a dataset is not bell shaped? - the range is equal to 6 SD -the range is larger than the interquartile range - the mean is much smaller than the median -there are no outliers

The mean is much smaller than the median

A researcher is testing the hypotheses below: Ho: mu = 100 Ha: mu < 100 After summarizing a very large dataset, the test statistic is calculated to be -1.85 and the p-value is 0.03. What is the correct interpretation of this p-value?

The probability of getting a t-statistic of -1.85 or smaller, assuming the null hypothesis is true, is 0.03.

A researcher is testing the hypotheses below: Ho: mu = 100 Ha: mu < 100 After summarizing a very large dataset, the sample statistic (x-bar) is 98 and the test statistic is calculated to be -1.85. Choose the correct interpretation of the test statistic below.

The sample statistic of 98 is 1.85 standard deviations below the null value of 100.

An experiment was conducted to compare the mean lengths of time required for the body to absorb two drugs (A and B). Ten people were randomly selected and assigned to receive one of the drugs. The length of time (in minutes) for the drug to reach a specified level in the blood was recorded. What is the explanatory variable in this study?

The type of drug (A and B)

Does support for new national parks (For or Against) differ by region in the country (West, Midwest, South, Northeast)? Choose the correct inference procedure to answer this question.

Use a chi- square test of association

In a time study conducted at a manufacturing plant, the length of time to complete a specified operation is found to have a bell-shaped distribution with mean of 12.8 and standard deviation of 1.7. Which of the following statements is true? -About 50% of the data set is greater than 11.1 -About 99.7% of the data set lies between 7.7 and 17.9 -About 68% of the data set lies between 9.4 and 16.2 -About 95% of the data set lies within 3 standard deviations of the center

b. ABout 99.7 of the data

binomial or not? X = number of heads from flipping the same coin ten times, where the probability of a head = ½

binomial, n=10 and p=0.5

Consider the hypotheses below: Ho: mu = 54 Ha: mu not equal 54 The test statistic was calculated to be -1.55, with a p-value of 0.12. Which of the pictures below is the correct illustration of the p-value?

both sides x axis- -1.55 0.06

What would happen to the width of a confidence interval if the sample size was increased from 50 to 100?

confidence interval would get narrower

A high-school teacher wants to estimate with 99% certainty the mean number of calories in the school lunch provided by the school district. What should she do?

construct a 99% confidence interval for a single pop mean

In 1988, a sample of 22,071 male physicians were randomly assigned to take either an aspirin or a placebo. The group that took the placebo is known as the

control group

is your overall satisfaction with a hotel room correlated with the cost of the room? You are provided with the following regression equation based on data collected on room prices and customer satisfaction ratings: Rating = 4.55 - 0.25*Price. What is the correct interpretation of the slope?

for every one unit increase in price there is a 0.25 unit decrease in average rating

Do scores on a test of math achievement exceed the recommended minimum of 76% for eighth-graders in Maryland? Choose the correct inference procedure to answer this question

hypothesis test for one population mean

A 95% confidence interval was constructed to estimate the mean difference in IQ scores between older and younger spouses. The interval is (-3.6 to 2.1). If the hypotheses below were tested, Ho: mu(d) = 0 Ha: mu(d) >0 would you find significance?

no the interval includes 0

The USA Today AD Track (3/1/00) examined the effectiveness of the new ads involving the Pets.com Sock Puppet (which is now extinct). In particular, they conducted a nationwide poll of 428 adults who had seen the Pets.com ads and asked for their opinions. They found that 36% of the respondents said they liked the ads.If you wanted to cut the margin of error in half the next time you took a poll like this, what sample size would you need? A) One that is twice the size of what it was before. B) One that is half the size of what it was before. C) One that is a quarter the size of what it was before. D) None of the above

none of the above

When a representative sample is selected but only a small proportion contacted actually participate in the study, the problem is called

nonresponsive

X = number of cities in which it will rain tomorrow among five neighboring cities located within 10 miles of each other.

not binomial because trials arent independent

Consider the sampling distribution of the sample proportion. For the normal approximation to hold which of the following conditions must be satisfied:

np and n(1-p) must each be at least 10.

A teacher wants to know whether the number of hours students spend studying in a group affects the final course grade. He carries out a study as follows: Each student keeps a log of the hours he or she spends studying in a group and reports the total hours after the course is completed. This study is

observational study

Which of the following values would indicate the strongest linear relationship between two quantitative variables?

r=0.85

A survey based on a random sample of 1000 students found that 1% of these students, when asked by the professor doing the survey, admitted to having cheated on at least one exam. The results of this study, if applied to all students in the university, are questionable because of

response bias

A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The mean of the 10 strength measurements for the last hour was found to be 21 pounds per square inch. The statistical summary of 21 pounds per square inch is a

sample statistics

The __________ for a statistic is the probability distribution of possible values of the statistic for repeated samples of the same size taken from the same population.

sampling distribution

*diagram* high to low

skewed to the right

A survey was conducted to learn about the cell phone activities of cell phone users in the US. We found that 52% of cell phone users surveyed used their phones to send or receive email. Similarly, 49% of cell phone users surveyed said they used their phones to get directions. The margin of error both percentages is 2.4%. Which of the statements below is TRUE, statistically speaking?

statisitcally, speaking, we cannot say with confidence that less than half of all US cell phone users use their phones to send or recieve emails

Study I: a researcher studies the difference in heart diseases in Asian and Latin American people. Study II: a researcher randomly selects two groups of students (a control group and a treatment group) and give normal diet to the control group and vegetarian diet to the treatment group to study differences in short-term memory effects of diet. What studies are used in Studies I and II?

study 1 : observational study 2 : randomizzed experienment

The multiplier for a confidence interval involving proportions is determined by

the desired level of confidence

A cell phone company examined the effectiveness of a new ad campaign. In particular, they wanted test whether more than 1/3 of viewers approved of the ads. The company conducted a nationwide poll of 428 adults who had seen the ad and asked for their opinions. They found that 36% of respondents said they liked the ads. Suppose you increased the sample size for this poll to 1000, but you had the same sample percentage who like the ads (36%). How would this change the p-value of the hypothesis test you want to conduct?

the new p value would be smaller than before

p-value+0.003

there is NO relationship in the population

A researcher is testing the hypotheses below: Ho: mu = 100 Ha: mu < 100 After summarizing a very large dataset, the test statistic is calculated to be -1.85 and the p-value is 0.03. Which kind of error is possible?

type 1 error

Consider the question of whether a majority of university professors watched the super bowl. Suppose that you study a simple random sample of 80 professors and that 52 of them watched the superbowl this year. Let p=probability that a randomly selected professor watched the super bowl. We test the hypotheses: Ho: p=.5 Ha: p>.5 Which of the illustrations below correctly show one way to calculate the p-value?

x axis- 0.5 at 0.65 = 0.000067

Are Physics majors less likely than Math majors to be enrolled in the honors program? Faculty at Harvard sampled students from both departments and constructed a confidence interval to estimate the difference in the proportion of students in the honors program y when comparing Physics majors to Math majors. The 95% confidence interval is (-0.15 to -0.02). Can you conclude that the proportion of Physics majors in the honors program is lower than the proportion of Math majors??

yes bc 0 is not included in the interval