1. An advertiser is experimenting with a new color scheme and conducts a study to test its effectiveness. In which situation could they use the two-sample t-test for comparing two population means?

They randomly expose consumers to one website when they land on their page: the old one with the original color scheme or the new one with the updated color scheme. Then they measure to see how much people buy.

They track each customer's spending habits in the old platform and then they change the color scheme to see if spending habits go up or down for each consumer.

They show consumers both options: the original color scheme or the updated color scheme. They let consumers decide which one they like better and then select the color scheme that most customers prefer.

2.

College Students and Depression: A public health official is studying differences in depression among students at two different universities. They collect a random sample of students independently from each of the two universities and administer a well known depression inventory. A score of 5 or above indicates some depression. A score above 15 indicates that active treatment is necessary. Sample Statistics Size(n) Mean () SD(s) Sample 1 50 9.2 .85 Sample 2 45 8.7 1.2 The official conducts a two-sample t-test to determine whether these data provide significant evidence that students at University 1 are more depressed than students at University 2. The test statistic is t = 2.64 with a P-value 0.005. Which of the following is an appropriate conclusion? The samples provide significant evidence that students at University 1 are more depressed than students at University 2. The samples do not provide statistically significant evidence. We can not use the t-test in this case because the variables (depression scores) are likely skewed to the right at each university.Analyses were run. The following is the (edited) output for the test: Hypothesis Test Results H1: Dance Scores: Coached Previously H2: Dance Scores: Not Coached Previously Difference Sample Mean Std. Err. DF T-Stat P-Value H1 - H2 .11 0.67168 94.155815 0.163767 0.4351 From the output we learn that: the data do not provide sufficient evidence to reject Ho; thus, we cannot conclude that the mean score of the students coached is higher than that of students never coached. the data provide sufficient evidence reject the Ho; thus, we cannot conclude that the mean score of the students coached is higher than that of students never coached. the data do not provide sufficient evidence reject the Ho; thus, we can conclude that the mean score of the students coached is higher than that of students never coached. the data provide sufficient evidence to reject Ho; thus, we can conclude that the mean score of the students coached is higher than that of students never coached