Inference Methods For each of the following descriptions, select the letter of the inference method you would use. (It is possible for a method to be used more than once or not at all.)

1. Student’s t for a mean

2. one-proportion z

3. χ2 goodness-of-fit

4. two-proportion z-test

5. paired t

1. Ithaca garbage bags In Ithaca, New York, every garbage bag must be tagged and not exceed 20 lb in weight. The city wants to know whether residents comply with the rules. One day, a truck driver randomly selected 135 bags left on the curb and weighed them. The driver found a mean weight of 21.5 lb with a standard deviation of 4 lb. Are Ithacans complying with the rule?

2. Google flu prediction The Centers for Disease Control and Prevention (CDC) gathers data from physicians and publishes the number of flu cases two weeks later. Researchers at Google recorded the number of flu-related queries and constructed an estimate of flu incidence that was immediate because it didn’t depend on reports from physicians. Google used its method to predict the number of flu cases for each week of the flu season and compared that prediction to the actual number of cases reported (two weeks later) by the CDC. Did Google’s predictions match the actual counts?

3. Gambling students A sample of 1979 college students completed the South Oaks Gambling Screen and Interpersonal Guilt Questionnaire and answered questions about their substance use. Students who were identified on the Gambling Screen as pathological gamblers (n=145) were matched to non–problem gamblers with respect to demographics and substance use to see whether there was any difference in guilt (as assessed by the Guilt Questionnaire). Pathological gamblers had significantly higher interpersonal guilt than their non–problem-gambling peers.

4. Vitamin D and colds Researchers randomly assigned 322 healthy adults in New Zealand to take either a placebo or a high dose of vitamin D. Researchers had hoped to show that vitamin D could prevent or reduce the symptoms of colds. But after 18 months (including two winter seasons), the proportion of participants suffering from an upper respiratory infection was no lower in the vitamin D takers than in those who took the placebo. (Source: JAMA 308:1333, 2012)

5. Gallup Poll bias? Polls of voters taken just before an election have the special feature that after the election, we learn the true population proportion (vote percentage for each candidate) that they were attempting to estimate. The Gallup Poll has been criticized for reporting values that were biased in favor of Republican candidates. Did their final prediction for the presidential election come close enough to the true value, or is there evidence that their methods are faulty?