Question

please answer a - e

STAT 3090 Lecture Notes Chapter 10 A researcher wishes esearcher wishes to determine whether fulltime college students get an amount of sleep different than the recommended eight hours ent than the recommended sieht hours per nicht. He takes a random sample of 52 full- hege students and finds the average number of hours slept per night to be 7.2 hours standard deviation of 1.27 hours. Does the researcher have evidence at the 5% level that college students do not sleep eight hours per night? (a) Define the parameter of interest and state the hypotheses. LITE (b) State and check whether the necessary assumptions hold. (c) Compute the test statistic and a corresponding p-value. (d) Provide support for your decision about the null hypothesis. (e) Summarize the results of your test.

Answer 1

amount of sleep X: The amount of sleep in hours all: The college students get an - eight hours per night l=8 hours X = The college steedents find the averge number of hours slept per night X = 7.2 hours n= The number of full time college students. n=52 r = standard deviation r=1-27 hours d = level of significance

Here we want to test that whether e students get an amount of sleep recommended eight hours per night the full to different than the or not it. null hypothesis - Ho: el=8 vs alternative hypothesis HA ll + 8 ie. Hoil = 8 vs HA ll #8 - - I Assumption Here we use z test The assumptions for z test 0 The data are continuous : Here The number of hours the students slept is continuous variable :. The data is continuous. ③ The data follow the normal probability distribution Here the number of full time college students is 52 which is greater than to Theis deda by CLT Ccentral limit theorem) This dato follows normal probability distribution & The sample is a simple random sample from its popierini Here takes a random sample of 52 full time college students Each individual has an equal probability of being selected The population standard deviation is known Here standard deviation = 1,27 (given i e known) 4

i data holds all the necessary assumptions 6 test statistic o di I = x - ll cat - 7.2-8 1.27 -0.8 0.1761

P-value = P lz 7 call P-value p-value = 2(0.0000028) = 0.00000 56 = o d Decision Reject Ho if p-value < x=0.05 Here P-value = 0 ca=0.05 we refect Ho - e conclusions we may conclude that the deta supports that - The Full night college students get an amount of sleep different than the recommended eight hours peo night