Question

ONLY a and b at the end

Q8: New York is known as "the city that never sleeps". Suppose the amount of sleep (in hours) is nearly normal. A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. Do these data provide strong evidence that New Yorkers sleep less than 8 hours a night on average? Assume the significant level is α-0.05. in max 257.73 0.77 6.179.78 Step 1: Parameter of interest: average amount of sleep of New Yorkers (mean of one population). Step 2: What is the null hypothesis? Step 3: What is the alternative hypothesis? Step 4: What is the test statistic? Step 5: We will reject Ho if the p-value the significance level α. (Fill the blank using " ", "-", Step 6: Step 7: Compute the test statistic based on the current sample. Compute the p-value, and make a decision. For the above problem Q8, answer the following questions. (a) What is the type I error rate of the test if the significance level is α? (b) What is the power of the test if the sample is i.i.d. from N(7.5,1)? What is the power of the test if the sample is 1.1.d. from N(7,1)? Assume the significant level is α 0.05.

Answer 1

iven data houYç Population mean parame tey of rt ere st of new ejorkess Averace amount of sleep pothesis Ho : olternative ) -test Statistic- - valuLL L gni

-1. TS32. than,-the Deci Sion:- pcal < p So jet tha nt Canclusion- Thei^ 4 Suf ficien evidonce to uppoth Clain -that, new yorkes sleep lesthanhours a night