Problem 11: Multiple choice This exercise consists of 4 multiple-choice problems that reflect the types of problems you may expect to see on the midterm exam. 11.1 Which of the following assumptions are NOT necessary in order to build a confidence interval for the sample mean (as discussed in class)? (a) The observations are independent. (b) The observations are randomly sampled. (c) There are at least 1000 samples. (d) All of these assumptions are necessary. 11.2 The sample mean of a dataset is X = 46. Which of the following is a possible confidence interval for X? (a) (42, 50) (b) (41, 65) (c) (40, 49) (d) Cannot be determined from the information given 11.3 To compare two cleaning products, you test each for the percentage of bacteria killed by each cleaning product. Let pA be the percentage for cleaner A and similarly pB for cleaner B. In the end, you compute a difference in means confidence interval to be (0.05, 0.1). Which of the following BEST describes a valid conclusion based on this study? (a) There is significant evidence that cleaner A outperforms cleaner B. (b) There is significant evidence that cleaner B outperforms cleaner A. (c) There is not enough evidence to conclude that one cleaner outperforms the other. 11.4 A company is testing a new ad to make sure it works as intended. The company recruits 500 customers at random, and assigns them to treatment and control groups at random. Each group has equal size and the spending habits of each customer are tracked for 10 days. The control group is shown an irrelevant ad from an unrelated company. You may assume everyone participates, there is no missing data, and no one drops out of the study (i.e. the study design and execution is not an issue). Which of the following are plausible sources of randomness in the data? The correct answer contains ONLY plausible sources of randomness, but may not be exhaustive. (a) The sample size and the size of each group. (b) The sample size, the size of each group, and the customer spending levels. (c) The sample of participants and the sample size. (d) The sample of participants, the treatment/control groups, and the customer spending levels. 1