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 Ho: µp = PT H1:µp < PT O Ho: PF PT H1:PF < PT O Ho:µF = HT H1:µp > PT O Ho: HF HT H1:µF + HT O Ho: PF PT H1:pF > PT %3D O Ho:PF = PT H1:PF + PT b) Determine the test statistic. Round to two decimals. t = c) Find the p-value and round to 4 decimals. d) Make a decision. O Fail to reject the null hypothesis O Reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. O There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college.

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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 Ho: µp = PT
H1:µp < PT
O Ho: PF
PT
H1:PF < PT
O Ho:µF = HT
H1:µp > PT
O Ho: HF
HT
H1:µF + HT
O Ho: PF
PT
H1:pF > PT
%3D
O Ho:PF = PT
H1:PF + PT
b) Determine the test statistic. Round to two decimals.
t =
c) Find the p-value and round to 4 decimals.
d) Make a decision.
O Fail to reject the null hypothesis
O Reject the null hypothesis
e) Write the conclusion.
O There is not sufficient evidence to support the claim that enrollement is high at a four-year college
than a two-year college.
O There is sufficient evidence to support the claim that enrollement is high at a four-year college than
a two-year college.
Transcribed Image Text: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 Ho: µp = PT H1:µp < PT O Ho: PF PT H1:PF < PT O Ho:µF = HT H1:µp > PT O Ho: HF HT H1:µF + HT O Ho: PF PT H1:pF > PT %3D O Ho:PF = PT H1:PF + PT b) Determine the test statistic. Round to two decimals. t = c) Find the p-value and round to 4 decimals. d) Make a decision. O Fail to reject the null hypothesis O Reject the null hypothesis e) Write the conclusion. O There is not sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college. O There is sufficient evidence to support the claim that enrollement is high at a four-year college than a two-year college.
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