Question

Short Answer

 9. Suppose that you and a friend analyze the same sample data and conduct a test of significance about the same conjectured value, but you use a two-sided alternative and your friend uses a onesided alternative. 

a. Will you and your friend obtain different values of the test statistic? Explain briefly.

 b. Will you and your friend obtain different values of the p-value? Explain briefly.

 10. The National Institutes of Health funded a study of a random sample of 856 people age 71 and older in the United States. They found that 9.7% of these people suffer from Alzheimer’s Disease.

 a. Identify the population of interest in this study. 

b. Is .097 (the decimal version of 9.7%) a parameter or a statistic? What symbol do you use to represent it? 

c. Determine a 95% confidence interval for the proportion of elderly Americans who have Alzheimer’s disease.

 d. Check and comment on whether the technical conditions required for this confidence interval are satisfied.

 e. If you were to determine instead a 90% CI, how would it differ and how would it be similar to the result in part c? (Do not bother to do the calculations.) 

f. Determine how many people would have to be studied in a new sample if you want to estimate the population proportion to within ± .02 with 99% confidence. (Use the result of the current sample in your determination of the new sample size.) 

11. Students in an introductory statistics class were asked how many states they have visited. The following output pertains to the sample results: 

a. Determine a 90% confidence interval for the population mean number of states visited among all students at this university.

 b. Check and comment on whether the technical conditions of this confidence interval are satisfied. 

c. For what proportion of students in the sample is the number of states visited within the interval calculated in part a?

 12. Explain (briefly) what is wrong with each of the following sets of hypotheses: a. Ho: ? = 1.2 Ha : ? >1.2 b. Ho: p ˆ = .5 Ha : p ˆ > .5 c. Ho: ? ≠ .5 Ha : ? = .5 13. Suppose you analyze data to assess whether the proportion of heart transplant deaths at St. George’s Hospital in London significantly exceeded the national benchmark rate of 15%.

 a. Write a sentence describing what committing a Type I error would mean in this study. 

b. Write a sentence describing what committing a Type II error would mean in this study. 

14. A student wants to assess whether her dog Muffin tends to chase her blue ball more often than she chases her red ball. The student rolls both a blue ball and a red ball at the same time and observes which ball Muffin chooses to chase. Repeating this process a total of 96 times, the student finds that Muffin chased the blue ball 52 times and the red ball 44 times.

 a. What are the observational units in this study? 

b. What is the variable in this study?

 c. State the appropriate null and alternative hypotheses, in words and in symbols.

 d. Calculate the test statistic and p-value. 

e. Would you reject the null hypothesis at the ? =.10 significance level? Explain. 

f. Write a one-sentence conclusion to the student, summarizing what the data reveal about whether her dog Muffin tends to chase her blue ball more often than her red ball. Include an explanation of what the p-value means in the context of this study. 

15. In a national study of American high school students in 2006, researchers asked students whether they have cheated on a test in the past year. Researchers found that 61.8% of the male students admitted to cheating, compared to 58.3% of female students.

 a. State the appropriate null and alternative hypotheses for testing whether the proportion of male students who admit to cheating is higher than that of female students. 

b. What further information would you need in order to conduct the test?

 c. Suppose the technical conditions are met and the test statistic turns out to be z = 6.32. Summarize the conclusion that you would draw from this test.

Answer 1

#9b

yes the p-values will be different

because for two-tail test, p-value = 2*(p-value of 1-tailed test)