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but just need the answer for just the last question plz (f)
< Previous question Next question ? Question 3 (of 4) You have answered 29 of 35 parts Jump to question: 1 2 3 4 It is thought that students living at home may spend a different amount of time studying than those living away from home. To test this hypothesis, a random sample of 200 students living at home (H) and a random sample of 150 students living away from home (A) was chosen, It was found that 104 of the students living at home and 45 of the students living away from home studied for more than 20 hours per week. Based on these findings and using a = 0.05, investigate whether or not there is a difference in the proportion of students studying more than 20 hours per week between those living at home and those living away from home. a) Select the appropriate null and alternative hypotheses for testing the study based hypothesis that students are equally likely to study for more than 20 hours per week whether they live at home or away from home. HO : ΠΗ = ΠΑ; HA: TH #ΠΑ OH :THETA HA: TH TA O HỘ : TTH TA # 0; HATA H : TH=TA; HA: PH = PA OH : Ah + TA; HA PH= PA TA = 0 The estimates of the proportions who study for greater than 20 hours for the two groups of students are: 05 (1) PH 0.52 DP 0.5 PA — 0.30 2 DP
OH :TH TA; HA: ph = PA OH : TAHA: pH = PA b) The estimates of the proportions who study for greater than 20 hours for the two groups of students are: (1) 0.5 PH = 0.52 2DP (ii) 0,5 PA = 0.30 2DP c) Using the pooled sample proportion, the standard error se for the difference between the two proportions is: 0.053 SDP d) The test statistic is: 1 4.12 3DP e) Using R the p-value for this test is: 1 0.000 SDP f) Given the p-value above select the appropriate conclusion to the hypothesis test: 1 o We have evidence to reject Ho in favour of the alternative hypothesis that there is a difference in the proportion of students studying more than 20 hours for those living at home or away from home. o We have evidence to reject H, in favour of the alternative hypothesis that the proportion of students studying more than 20 hours is lower for those living at home than those living away from home. We accept HA and conclude there is no evidence of a difference in the proportion of students studying more than 20 hours for those living at home or away from home. o We do not have sufficient evidence to reject H, i.e. there is no evidence of a difference in the proportion of students studying more than 20 hours for those living at home and those living away from home. We have evidence to reject H, in favour of the alternative hypothesis that the proportion of students studying more than 20 hours is lower for those living away from home than those living at home.
Question 3 Population ! M = 200 X = 104 PT Population 2 na = 150 = 4S = la loi ou 104052 200 P2 = 45 ISO =0.3 (6) PH = 0.53 PA= 0.3 (c) = x1 +02 ni +12 = 104 + 45 200 + ISO = 149 => 0.42571 350 |-0.42571+ = 057428 1 T-stat= ê pa ê + ni na 10.42571)(0.57428), (0.42571)(0.57428) 200 150 + = 0.0534 ( () (0.52-0-3) - 0 4.119 0.0534 (e) a porm ( 4.119, lower. fail = FALSE) ē 0.0000379 000