For questions 1 through 10, determine what the appropriate test you would use is.You do not have to test the hypothesis for these questions (1-10).For simplicity, I have left off the sizes of each sample.

Possible Answers:

Independent sample t-test with equal variance

Independent sample t-test with unequal variance

Dependent sample t-test

Z-test for proportions

1.Do people in 2020 wear masks (P=0.90) more frequently than did people in 2019 (P=0.01)?

2.Is there a difference in the number of close friends that Republicans and Democrats report having (and, respectively)?

3.Do engineering majors()study more hours a week than do philosophy majors()?

4.Do people commit fewer crimes after they get married () than they did before ()?

5.Do students taking SOC 3391 online () score better than those who took it in-person ()?

6.Do union workers()make more than non-union workers ()in manufacturing?

7.In a matched pair design, do COVID-19 patients taking dexamethasone spend less time in the hospital () than do those on the placebo treatment ()?

8.Do students who get to hear their favorite song score better on a test ()than do those who don't get to ()?

9.Do Apple+ subscribers maintain their subscriptions for longer ()than do Disney+ subscribers ()?

10.Are private schools more likely to shift online (31%) in 2020 than public schools (42%)?

For questions 11-15, answer the question andshow all intermediate values.

For independent sample t-tests: mean values for each sample, the variances for each sample, estimated standard error of the difference in means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For dependent sample t-tests: mean values for each sample, standard deviation for the difference between groups, standard error of the difference between means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For proportions: sample proportions, combined proportions, standard error of the difference, z-score, critical z-score, and your decision to reject or retain the null.

11.Joe Biden's favorability was 53% in a poll of 1343 voters[1]. From the same polling agency (Fox News), Trump's favorability was at 43% in a sample of 1000 voters. Test the null hypothesis that Biden and Trump have equivalent favorability ratings among voters (alpha=0.05).

1. General Cybernetics is testing whether its new exoskeletal augmentation increases strength. They measure how much people can lift (bench press) before and after using the new augment:

Lifting (before) Lifting (after)

180 250

200 300

170 280

190 370

200 240

180 320

170 410

185 215

190 240

220 510

Test the null hypothesis that the pre- and post-augment lifting amounts are equal (alpha=0.05).

13.To test whether individuals primed towards violence are more aggressive, researchers conducted an experiment. Subjects were shown either a violent sequence (treatment) or peaceful sequence (control) before engaging in a simulated game (N=10 for each). They measured the number of aggressive plays that the individual took. Those in the treatment group engaged in 4 violent plays on average (s = 0.8), while those in the control group engaged in 2 violent plays on average (s = 0.9). Test the null hypothesis that there is no difference in aggressive plays between the treatment and control groups (alpha = 0.05).

14.To understand the implications of universal basic income (UBI) on individual economic hardships, researchers leverage a natural experiment where people signed up for Andrew Yang's offer and then were randomly selected to receive it or not. Using the data below on the number of economic hardships (difficulty paying rent/mortgage, electric bills, other utility bills, health care bills, etc.),test whether individuals with UBI have different number of economic hardships than those without it (alpha=0.1, two tails).

No UBI UBI

3 4

0 4

1 2

0 2

1 3

15.Researchers are interested in whether having an older sibling provides people a model for drug use in adolescence. They gather random samples of people with either older siblings or not and measure their average age of first drug use. For individuals with no older siblings (N=16), they find an average age at first drug use of 17.5 (s=1.4) For individuals with older siblings (N=20), they find an average age at first drug use of 16.7 (s=0.8).Test the null hypothesis that the average age of first drug use is the same between those with an older sibling and those without (alpha=0.05).