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)