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 6,954 with a standard deviation of 598. Of the 35 two-year colleges surveyed, the mean enrollment was 4,668 with a standard deviation of 606. Test the student's claim at the 0.01 significance level.

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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 6,954 with a standard deviation of 598. Of the 35 two-year colleges surveyed, the
mean enrollment was 4,668 with a standard deviation of 606. Test the student's claim at the 0.01
significance level.
Preliminary:
a. Is it safe to assume that
N4yr
< 5% of all students enrolled at a 4-year college in the Unites States and
< 5 % of all enrolled at a 2-year college in the Unites States?
nzyr
No
O Yes
b. Is n4yr > 30 and n2yr
30 ?
O No
Yes
Test the claim:
a. Determine the null and alternative hypotheses.
Ho: HAyr ? v H2yr
Ha: H4yr ? v H2yr
b. Determine the test statistic. Round to four decimal places.
t
c. Find the p-value. Round to 4 decimals.
p-value =
d. Make a decision.
O Reject the null hypothesis.
OFail to reject the null hypothesis.
e. Write the conclusion.
O There is sufficient evidence to support the claim that enrollement is higher at a four-year
college than a two-year college.
O There is not sufficient evidence to support the claim that enrollement is higher 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 6,954 with a standard deviation of 598. Of the 35 two-year colleges surveyed, the mean enrollment was 4,668 with a standard deviation of 606. Test the student's claim at the 0.01 significance level. Preliminary: a. Is it safe to assume that N4yr < 5% of all students enrolled at a 4-year college in the Unites States and < 5 % of all enrolled at a 2-year college in the Unites States? nzyr No O Yes b. Is n4yr > 30 and n2yr 30 ? O No Yes Test the claim: a. Determine the null and alternative hypotheses. Ho: HAyr ? v H2yr Ha: H4yr ? v H2yr b. Determine the test statistic. Round to four decimal places. t c. Find the p-value. Round to 4 decimals. p-value = d. Make a decision. O Reject the null hypothesis. OFail to reject the null hypothesis. e. Write the conclusion. O There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college. O There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.
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