Name: ______Date: ______

1. A study is designed to determine whether grades in a statistics course could be improved by offering review material. The 250 students in an introductory statistics class are also enrolled in one of 20 lab sections. The 20 lab sections are randomly divided into 2 groups of 10 lab sections each. The students in a set of 10 lab sections are given extra review material during the last 15 minutes of each lab session. The students in the remaining 10 lab sections receive the regular lesson material, without the review material. The grades of the students who reviewed were higher, on average, than the students who did not review. What type of study is this?

A) An observational study. B) An experiment, but not a double-blind experiment.

C) A double-blind experiment. D) A matched-pairs experiment.

2. A sample of employees of a large company has been obtained. The length of time (in months) they have worked for the company was recorded for each employee. A stemplot of these data is shown below. In the stemplot 6|2 represents: 62 months.

What would be a better way to represent this data set?

A) Display the data in a time plot. B) Display the data in a boxplot.

C) Split the stems. D) Use a histogram with class width equal to 10.

Use this to answer question 3. Volunteers for a study were divided into 3 groups. Group 1 listened to Western religious music, group 2 listened to Western rock music, and group 3 listened to Chinese religious music. The blood pressure of each volunteer was measured before and after listening to the music, and the change in blood pressure (blood pressure before listening minus blood pressure after listening) was recorded.

3. What could we do to graphically explore the relationship between type of music and change in blood pressure?

A) See if blood pressure decreases as type of music increases by examining a scatterplot.

B) Make a histogram of the change in blood pressure for all of the volunteers.

C) Make side-by-side boxplots of the change in blood pressure, with a separate boxplot for each group.

D) Do all of the above.

Use the following to answer 4-5. Many residents own more than one car but consider one of their cars to be the main family vehicle. The age of these family vehicles can be modeled by a normal distribution with mean 2 years and standard deviation 6 months.

4. What percentage of family vehicles are between 1 and 3 years old?

A) Cannot be determined based on the information given.

B) 68% C) 95% D) 99.7%

5. What is the standardized value for a family vehicle that is 3 years and 3 months old?

A) 0.22 B) 2.5 C) 2.6 D) 2.92

6. A free screening program is set up in the downtown area. People can walk in and have their cholesterol measured. 173 people use the service, and their average cholesterol is 217.8. The value 217.8 is an example of ______

A) a sample proportion. B) a statistic.

C) a parameter. D) an unbiased parameter.

7. As cheese matures, a variety of chemical processes take place. The taste of cheese is related to the concentration of several chemicals. In a study of cheese in a certain region, samples of cheese were analyzed for lactic acid concentration and were subjected to taste tests. The numerical taste scores were obtained by combining the scores from several tasters. A scatterplot of the observed data is shown below.

What is a plausible value for the correlation between lactic acid concentration and taste rating? A) 0.999 B) 0.7 C) 0.07 D) –0.7

Use this to answer # 8. We are studying the relationship between sugar consumption and weight. 12 people are randomly assigned to one of two groups. The first group of 5 people is put on a low sugar diet and the second group of 7 participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant.

8. Which of the following basic principles of statistical design was not used in this experiment? A) control B) randomization

C) repetition D) blinding

9. Which of the following sets of four numbers has the largest standard deviation?

A) 7, 8, 9, 10 B) 5, 5, 5, 5 C) 0, 0, 10, 10 D) 0, 1, 2, 3

Use the following to answer question 10. The Michigan Department of Transportation (M-DOT) is working on a major project: 80% of the highways in Michigan need to be repaved. To speed completion of this project, many contractors will be working for M-DOT. Contractors are currently bidding on the next part of the project. To help make a decision about which contractor to hire, M-DOT collects many variables besides just the estimated cost. One of those variables is the contractor's estimate of the number of work days required to finish the job. Twenty contractors have bid on the next job. The boxplot below represents their estimates of the number of work days required.

10. What is (approximately) the interquartile range, based on the boxplot?

A) 140 days B) 270 days

C) 360 days D) 760 days

Use the following to answer # 11-12.

Twelve people, who suffer from chronic fatigue syndrome, volunteer to take part in an experiment to see if shark fin extract will increase one's energy level. Eight of the volunteers are men and four are women. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. We wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other.

11. For which reason is a block design appropriate in this experiment?

A) Gender equity is an important legal consideration in this study.

B) We believe men and women may respond differently to treatments.

C) We want the conclusions to apply equally to men and women.

D) All of the above.

12. Suppose one of the researchers is responsible for measuring if a subject displays an increase in energy level. What design principle should be added to this experiment?

A) Two placebos.

B) Use a stratified sampling design to assign subjects to treatments.

C) Use fewer subjects but observe them more frequently.

D) Conduct the study as a double-blind experiment.

Use the following to answer # 13. An opinion poll in Ohio is used to determine whether registered voters in the state approve of a measure to ban smoking in public areas. They select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure.

13. What type of sampling method was used to collect the data?

A) A systematic county sample. B) A stratified sample.

C) A multistage sample. D) A simple random sample.

Use this to answer # 14-15. 100 volunteers who suffer from depression are available for a study. 50 are selected at random and are given a drug that is thought to be particularly effective in treating depression. The other 50 are given an existing drug for treating depression. A psychiatrist evaluates the symptoms of all volunteers after 4 weeks to determine if there has been substantial improvement in the severity of the depression.

14. What is the explanatory variable or factor in this study?

A) Which drug the volunteers receive.

B) The use of randomization and the fact that this was a comparative study.

C) The extent to which the depression was reduced.

D) The use of a psychiatrist to evaluate the severity of depression.

15. In which situation would this study be double-blind?

A) Neither drug had any identifying marks on it.

B) Volunteers were not allowed to see the psychiatrist nor was the psychiatrist allowed to see the volunteers during the session when the psychiatrist evaluated the severity of the depression.

C) Neither the volunteers nor the psychiatrist knew which treatment any person had received.

D) All of the above.

16. A distributor is doing a customer satisfaction survey for a manufacturer of DVD players. A sample of 68 clients is asked to rate a DVD player on ease of use, on a 1 to 10 scale, where 1 corresponds to the worst rating and 10 to the best possible rating. A bar graph of the ease of use ratings classified by gender is given below.

What percentage of the sampled female clients rated the DVD player as not so easy to use (a rating of 4 or lower)?

A) 28% B) 29%

C) 38% D) 62%

Use the following to answer # 17.. The number of undergraduates at Johns Hopkins University is about 2000, while the number at Ohio State is approximately 40,000.

17. Say the actual proportion of undergraduates at Johns Hopkins University who feel drinking is a problem among college students is 67%. A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled felt that drinking was a problem among college students. Which value(s) can be labeled as parameter(s)? A) 60% B) 67% C) 60% and 67% D) 50

Use this to answer # 18. The Consumers Union measured the gas mileage of 38 cars from the 1978–79 model-year on a test track. The pie chart below provides information about the number of cars from each country in this study by the Consumers Union.

18. What conclusion can we draw based on this pie chart?

A) Italian cars get significantly lower gas mileage than cars of other countries.

B) More than half of the cars in the study were from the United States.

C) Swedish cars get gas mileages that are between those of Japanese and U.S. cars.

D) Audi, Porsche, and BMW represent approximately a quarter of the cars tested.

Use the following to answer question 19.

19. Data on the mileage of 20 randomly selected cars is listed below. The values are ordered for convenience.

12 / 13 / 15 / 16 / 16 / 17 / 18 / 18 / 19 / 1920 / 20 / 22 / 23 / 24 / 26 / 26 / 27 / 27 / 29

What is the median mileage for these 20 cars?

A) 17.5 miles/gal B) 19 miles/gal C) 19.5 miles/gal D) 20 miles/gal

20. The average salary of all female workers is $35,000. The average salary of all male workers is $41,000. What must be true about the average salary of all workers?

A) It must be $38,000. B) It must be larger than the median salary.

C) It could be anything from $35,000 to $41,000. D) It must be > $38,000.

21. A paper interviews an expert about a proposed system for rating the teaching ability of faculty members. He says, “The evidence indicates that the correlation between a faculty member's research productivity and teaching rating is close to zero.” What would be a correct interpretation of this statement?

A) Good researchers tend to be poor teachers and vice versa.

B) Good teachers tend to be poor researchers and vice versa.

C) There isn’t much relationship between teaching and research accomplishment.

D) Good research and good teaching go hand in hand.

22. In a study of 1991 model cars, a researcher computed the regression line of price (in dollars) on horsepower. He obtained the following equation for this line.

price = –6677 + 175 * horsepower. Based on the least-squares regression line, what would we predict the cost of a 1991 model car with horsepower equal to 200 to be?

A) $41,677 B) $35,000 C) $28,323 D) $13,354

23. A sample of 16 people is taken and their weights are measured. The standard deviation of these 16 measurements is computed to be 5.4. What is the variance of these measurements?

A) 2.24 lbs. B) 2.24 lbs2. C) 29.16 lbs. D) 29.16 lbs2.

24. To see if smoking causes cancer, researchers surveyed a large sample of adults. For each they recorded whether the person had smoked regularly at any period in their life and whether the person had cancer. They compared the proportion of cancer cases in those who had smoked at some time in their lives with the proportion of cases in those who had never smoked at any point in their lives. The researchers found that there was a higher proportion of cancer among those who had smoked than among those who had never smoked. What type of study is this?

A) An observational study. B) An experiment, but not a double-blind experiment.

C) A double-blind experiment. D) A block design.

The correlation between length and width is calculated to be r = 0.827.

25. In the plot, notice that length is treated as the response variable and width as the explanatory variable. Suppose we had taken width to be the response variable and length to be the explanatory variable. What would be the correlation between width and length in this case? A) 0.827 B) –0.827 C) 0.000

D) Something between 0.827 and –0.827, but we cannot determine the exact value.

**Answer Key - Exam 1**

1. B

2. C

3. C

4. C

5. B

6. B

7. B

8. D

9. C

10. B

11. B

12. D

13. B

14. A

15. C

16. C

17. B

18. B

19. C

20. C

21. C

22. C

23. D

24. A

25. A