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For questions 11-15, answer the question and show all intermediate values for full credit. 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. Clearly label all values and round them to 2 decimal places (e.g., 2.57 instead of 2.5702 or 2). Do not round critical t or z values from your tables. 11. Dating app researchers want to determine the effects of the first profile picture. In a sample of 25 users with headshots as their profile picture, they find an average response rate of 30%. In a sample of 25 users with group shots as their profile picture, they find an average response rate of 17%. Test the null hypothesis that headshots and group shoots receive equal response rates (alpha=0.05). 12. Researchers are interested in whether early voters are more informed than those who vote on Election Day. After sampling from each group, they gave a test of election knowledge and counted the number of correct items. In the sample of 20 early voters, the average number of correct items was 7.1 (s - 1.1). In the sample of 20 Election Day voters, the average number of correct items was 5.4 (s - 2.3). Test the null hypothesis that the average number of correct items was the same between early and Election Day voters (alpha-0.05). 13. Education researchers wonder if the age of children in a classroom influences how their teachers rate them. They ask teachers to rate the behavior of their students, with higher scores indicating better behavior. For younger students in the class, teachers rated their behavior as 15.92 (N = 10, s = 1). For students the typical age in the class, teachers rated their behavior as 15.01 (N=10, s = 1.05). Test the null hypothesis that the average behavior rating was the same between young and typical age students in a class (alpha-0.05). 14. A family researcher is interested in whether attending a parenting class leads families to spend more time together. She measures the number of times a week the family has dinner together before and after the classes. Dinners Dinners Together Together (Before) (After) N W N W W J O NO Test the null hypothesis that the pre- and post-class scores are equal (alpha-0.05). 15. A number of businesses are currently struggling with whether to force their workforce to return to the office or allow them to continue working from home. To determine what, if any, effects working from home has on productivity, one such company measured daily task completion for a set of their workers, some working from home and others working in the office. The results of their data collection are in the attached dataset This dataset (Module 10_wth) has the following variables: Office: Daily tasks completed for workers in the office After: Daily tasks completed for workers from home Using this data and the appropriate statistical test, determine if work location is associated with a difference in tasks completed. Use alpha - 0.05 and a two-tail test, You must include program output from SPSS/Excel in addition to your