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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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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