# a researcher wants to see whether there is a significant

Male |
Female |

n = 28 |
n = 24 |

A researcher wants to see whether there is a significant difference in resting pulse rates for men and women. A summary of the data she collects is displayed in the table on the left. Let μ_{m}represent the mean resting pulse rate for males andμ_{f}represent the mean resting pulse rate for females. Use this information for problems 1 – 4.

1. What are the appropriate hypotheses for the researcher to use to test for a significant difference?

2. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.

3. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis.

4. What is the conclusion of the test in the context of this problem?

To study the effectiveness of a drug for arthritis, two samples ofpatients were randomly selected. One sample of 100 was injectedwith the drug, the other sample of 60 receiving a placebo injection.After a period of time the patients were asked if their arthriticcondition had improved. Perform a four step hypothesis test to test whether the drug improved arthritic condition (that is, test to see if the proportion of patients who improved is higher for those who used the drug).Use this information for problems 5 – 8.

5. What are the appropriate hypotheses for the researcher to use?

6. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.

7. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis.

8. What is the conclusion of the test in the context of this problem?

Mars, manufacturer of M&Ms candies, used to publish the distributions of colors for M&Ms but no longer does that. Someone gathered the colors for a large number of M&M and they are reported in the table. Perform a four step hypothesis test to determine if there are equal numbers in each color.

Use this information for problems 9 – 12.

9. What are the appropriate hypotheses for the researcher to use?

10. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.

11. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis.

12. What is the conclusion of the test in the context of this problem?

An economist wants to test whether mean housing prices are the same regardless of which of 3 air-pollution levels typically prevails. A random sample of house purchases in 3 areas yields the price data below. Perform a four step ANOVA and use the information for problems 13 –16.

13. What are the appropriate hypotheses for the researcher to use?

14. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.

15. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis.

16. What is the conclusion of the test in the context of this problem?

Use the following information to answer questions 17 and 18.

A random sample of 30 couples who were also new home ownerswereasked to report the cost of their first house and their combined age when they married. Theoutput of a regression analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are satisfied.

17.What is the slope of the regression line? Write an interpretation of the slope in context.

18. Test the hypothesis that the slope is zero (significance level is 0.05), then choose the correct decision regarding the null hypothesis and write the statement that correctly summarizes the conclusion. Specify the value of the test statistic, the p-value, the decision for the test in terms of the null hypothesis, and write a conclusion for the test in context.

A high school girls cross country coach performs a regression to predict the finish times of runners in the 10k event from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Use this information for the remaining problems.

19. The coach wants to predict the finish time of his top runner who trained for 145 minutes the previous week. Should the coach use a confidence interval or a prediction interval? Explain why.

20. Suppose the coach’s top runner trained for 145 minutes the previous week. If this runner participates in the 10k event, what is the coach’s expected finish time for this runner? Explain your answer.

From the regression equation we can see that for the training time 145 minutes the

21. Can he be reasonably confident that this runner will beat the time she had at the last meet of 51 minutes? Explain.

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