Unteers were divided into two equal-sized groups. each volunteer took a math test that involved transforming strings of eight digits into a new string that fit a set of given rules, as well as a third, hidden rule. prior to taking the test, one group received 8 hours of sleep, while the other group stayed awake all night. the scientists monitored the volunteers to determine whether and when they figured out the rule. of the volunteers who slept, 39 discovered the rule; of the volunteers who stayed awake, 15 discovered the rule. what can you infer about the proportions of volunteers in the two groups who discover the rule? support your answer with a 90% confidence interval.

Stu and ambrose are working together on a study of whether diet is related to students' mental health. first, they randomly select 10 students from the student center and 10 students from the office of counseling and psychological services. then, they ask students to rate their diet in terms of healthiness on a scale of 1-100 before completing a 20-item mental health survey. a) name one of the constructs being studied b) how was the construct you named above operationally defined in this experiment? e) was the variable you described above their independent variable, their dependent variable, or a controlled variable? d) what is a confounding variable? what is a potential confound in this study?