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 6,215 with a standard deviation of 781. Of the 35 two-year colleges surveyed, the mean enrollment was 6,202 with a standard deviation of 613. Test the student's claim at the 0.01 significance level.Preliminary:Is it safe to assume thatn4yr≤5%n4yr≤5% of all students enrolled at a 4-year college in the Unites States andn2yr≤5%n2yr≤5% of all enrolled at a 2-year college in the Unites States?YesNoIs n4yr≥30 and n2yr≥30 ?NoYes Test the claim:Determine the null and alternative hypotheses. H0H0: μ4yr μ2yr HaHa: μ4yr μ2yrDetermine the test statistic. Round to four decimal places.t=Find the pp-value. Round to 4 decimals.pp-value = Make a decision.Fail to reject the null hypothesis.Reject the null hypothesis.Write the conclusion.There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.

Given Data : For Sample 1 x̄1 = 6215.0 s1 = 781.0 n1 = 35 For Sample 2…

Answered: student at a four-year college claims…

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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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 6,215 with a standard deviation of 781. Of the 35 two-year colleges surveyed, the mean enrollment was 6,202 with a standard deviation of 613. Test the student's claim at the 0.01 significance level.

Preliminary:

Is it safe to assume that

n4yr≤5%n4yr≤5% of all students enrolled at a 4-year college in the Unites States and
n2yr≤5%n2yr≤5% of all enrolled at a 2-year college in the Unites States?
- Yes
- No
Is n4yr≥30 and n2yr≥30 ?
- No
- Yes

Test the claim:

Determine the null and alternative hypotheses.

H0H0: μ4yr μ2yr
HaHa: μ4yr μ2yr
Determine the test statistic. Round to four decimal places.
t=
Find the pp-value. Round to 4 decimals.
pp-value =
Make a decision.
- Fail to reject the null hypothesis.
- Reject the null hypothesis.
Write the conclusion.
- There is not sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.
- There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.