1. Researchers Vogel et al. (JAMA, 2006) reported the following findings about the Study of Tamoxifen and Raloxifene (STAR), a study involving postmenopausal women who were at an increased risk for invasive breast cancer. Of the 9,726 women randomly assigned to use tamoxifen daily, 163 developed invasive breast cancer sometime during the next five years, compared to 168 in the group of 9,745 who were randomly assigned to use raloxifene daily.

A) Explain why it would be okay to use the theory-based method (that is, normal distribution based method) to find a confidence interval for this study.

a) We can use a theory-based approach because we have at least 10 successes and 10 failures.

b) We can use a theory-based approach because we have less than 10 successes and 10 failures.

c) We can use a theory-based approach because we have a sample size of less than 20.

or d) We can use a theory-based approach because we have a sample size of at least 20.

B) Use an appropriate applet to find and report the theory-based 99% confidence interval.Roundyour answersto 4 decimal places, e.g. 0.0083.

C) Interpret the 99% confidence interval in the context of the study.

a) We are 99% confident that the probability of developing invasive breast cancer with raloxifene is 0.0043 to 0.0053 lower than with tamoxifen.

b) We are 99% confident that the probability of developing invasive breast cancer with tamoxifen is up to 0.0052 lower to 0.0043 higher than with raloxifene.

c) We are 99% confident that the probability of developing invasive breast cancer with raloxifene is 0.0043 to 0.0053 higher than with tamoxifen.

or d) We are 99% confident that the probability of not developing invasive breast cancer with tamoxifen is up to 0.0052 lower to 0.0043 higher than with raloxifene.

D) Relatively speaking, is the 99% confidence interval narrow or wide? Explain why that makes sense.

a) the interval is pretty wide because the study involved small sample sizes

b) the interval is pretty narrow because the study involved large sample sizes

c) the interval is pretty wide because the results of the two drugs are very different

d) the interval is pretty narrow because the results of the two drugs are similar

2. Suppose you have a data set with the following summary statistics: lower quartile = 18, median = 22, upper quartile = 28. Which of the following numbers would be outliers according to the 1.5 IQR rule? (Choose all that apply.) 1, 4, 40, 45, or 46

3. Suppose we are testing two means using a two-sided test and get a p-value of 0.03. We also construct a 95% confidence interval from the same data. We would expect:

a) 0 to be in the confidence interval.

b) 0 to not be in the confidence interval.

c) 0.03 to be in the confidence interval.

d) 0.03 to not be in the confidence interval.

or e) There is no way to expect any specific value to be in or not be in the confidence interval.

4. What is an advantage of a standardized statistic (e.g. t-statistic) over a statistic that is not standardized (e.g. difference in means)?

a) Standardized statistics are much easier to calculate than those that are not standardized.

b) Standardized statistics allow us to determine p-values, whereas those that are not standardized do not.

c) Standardized statistics will always give smaller p-values than those that are not standardized, thus allowing for stronger evidence against the null.

or d) It is easier to estimate strength of evidence from a standardized statistic than it is from one that is not standardized.