QUESTION 1: Until 2002, hormone replacement therapy (HRT), estrogen and/or progesterone, was commonly prescribed to post-menopausal women. This changed in 2002, when the results of a large clinical trial were published.8506 women were randomized to take HRT, 8102 were randomized to placebo. 166 HRT and 124 placebo women developed invasive breast cancer. Does HRT increase risk of breast cancer? (P value = 0.03) From the information above...

a) Define all the parameters of interest

b) State the null and alternative hypotheses

c) What is informal description of the strength of evidence against H0

d) Are the results statistically significant?

e) State the formal decision about H0, using = 0.05

f) Conclusion in the context of the question

g) Calculate the statistics of interest

QUESTION 6: In 2012 the Centers for Disease Control and Prevention reported that in a random sample of 4,349 African Americans, 31% were Vitamin D deficient. A 90% confidence interval based on this sample is (0.30, 0.32). It is believed that among the general population of Americans 8% suffer from Vitamin D deficiency.

(a) Define the appropriate parameter

(b) State the appropriate hypotheses for testing the claim that among African Americans, Vitamin D deficiency occurs at a rate other than 8%.

(c) Does this confidence interval provide evidence that among African Americans Vitamin D deficiency occurs at a rate other than 8%?

(d) What significance level is being used to make this decision? Briefly justify your answer.

(e) Which type of error, Type I or Type II, could you have made in part (b)?

(f) Briefly justify your answer.

QUESTION 10: A consumer protection agency is testing a sample of cans of tomato soup from a company. If they find evidence that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is greater than 100 ppb (parts per billion), they will recall all the soup and sue the company.

a) Define all the parameters

b) State the null and alternative hypotheses.

c) What does a Type I error mean in this situation.

d) What does a Type II error mean in this situation?

QUESTION 11: For each statement below circle TRUE if the statement is true, otherwise circle FALSE.

(a) TRUE FALSE The p-value is the probability that the null hypothesis is true.

(b) TRUE FALSE The significance level represents the probability of making a Type II error.

(c) TRUE FALSE A statistical test uses data from a sample to assess a claim about a population.

(d) TRUE FALSE Decreasing the significance level of a hypothesis test (say from 5% to 1%) will cause the p-value of an observed test statistic to increase.

(e) TRUE FALSE Every hypothesis testing procedure comes with a guarantee that a correct decision will be made.

(f) TRUE FALSE If we decrease the chances of a Type I error occurring, than the chances of a Type II error occurring will increase.