Question

A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Of the 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Test the student's claim at the 0.10 significance level. a) The null and alternative hypothesis would be: O Hopp = PT H:PF > PT OH:up = HT H:up < UT OH: PF рт HPF + PT OHJp = per H:Hp + HT O Hopp HPF PT Ho: HT Hup > Ur рт b) Determine the test statistic. Round to two decimals.

Answer 1

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Given: - x: four-year colleges surveyed hoo-yeas colleges Queveyed n = 65 X=5466 8, = 8191 De = 35 Y = 5068 82 = 4777 Q=0.10 Here the claim is that mean enrollment at four year colleges i's higutoe than at two-year colleges tar الد = The hypothesi's is. correct option is F Holla allt H, Mell b) test statistice t = x - S ni +S? na 5466-5068 81912 85 47772 + 35 398 1602.7852 0.2483 0.25 t = 0.25

c) p-value = P(ts-Iteau ! ) = P(ts-10.24831) = P(+4-0.2483) 0.402825 0.4023 p-value = 0.4023 Test criterian :- If p-valu & then reject null hypothesis Here p-value=0.4023 7 &=0.10 80 correct option is b) Fail to reject nou hypothesia. d) e) The Correct option is o) There is not sufficient evidence to support the claim that envoltement is higle at a four-year college than Hoo-year college.
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