7. Confidence intervals for estimating the difference in population means Elissa Epel, a professor of health psychology at the University of California-San Francisco, studied women in high- and low-stress situations. She found that women with higher cortisol responses to stress ate significantly more sweet food and consumed more calories on the stress day compared with those with low cortisol responses, and compared with themselves on lower stress days. Increases in negative mood in response to the stressors were also significantly related to greater food consumption. These results suggest that psychophysiological responses to stress may influence subsequent eating behavior. Over time, these alterations could impact both weight and health. You are interested in studying whether students living in the dorms or students living off campus have higher cortisol levels. You ask a sample of m = 25 students living in the dorms and na = 30 students living off campus to record their afternoon cortisol levels for a week. The average cortisol level for students living in the dons was Ma = 0.259 pg/dl, with a standard deviation of s. = 0.131. The average cortisol level for students living off campus was Ma = 0.237 py/dl, with a standard deviation of sa = 0.128. To develop a confidence interval for the population mean difference is - us, you need to calculate the estimated standard error of the difference of sample means, S[MI My) - The estimated standard error is 5(MI MY) =. Use the Distributions tool to develop a 99% confidence interval for the difference in the mean cortisol level of students living in the dorms and students living off campus. t Distribution 0050 .0030 O An -3.0 -2.0 LO 2.0 3.0 -2.648 2.648The 99%% confidence interval is to This means that you are * % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is to This means that you are 7%% confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. The new confidence interval is than the original one, because the new level of confidence is than the original one