Problem 5. 8 points) Sleeping in class In a large lecture section of an Introductory Statistics class, the professor asked students to fill in a survey that recorded both whether they usually sit in the Front, Middle, or Back of the classroom (Seat, and how much sleep they typically get at night (Sleep). The table below summarizes the observed results for a random sample of 285 students who responded to the survey Seating Less than 6 hours Between 6 and 8 hours More than 8 hours Total Front 13 31 13 57 Midde 30 99 40 169 Back Total 9 52 35 15 59 165 68 285 1. We want to know if where a student sits is related to how much the study typically sleeps. Which statistical test should we use? A. t test for sample mean B. Z test for one population proportion C test of independence Dy goodness of fit test E. Randomization test for difference of two population proportions 2. What conditions must be met for the hypothesis test to be valid? A. The data must come from a simple random sample B. There must be at least 10 'success' and 10 failure observations C. There must be at least 3 levels of the categorical variable D. There must be an observed count of at least 5 for each cell in the table E. There must be an expected count of at least 5 for each cell in the table 3. Assume the conditions are met, and choose from the dropdowns to form the correct null and alternative hypotheses for this test. He The variables Seat and Sleep are 7 H. The variables Seat and Sleep are ? 3. State the degrees of freedom for this test 4. Under the nut hypothesis model, what is the expected count for students who sit in the back of the classroom and who report getting less than 6 hours of sleep per night? expected count & Calculate the contribution to the test statistic for students who sit in the back of the classroom and who report getting less than 6 hours of sleep per night. contribution 6. Calculate the test statistic for this hypothesis test