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 6,288 with a standard deviation of 585. Of the 35 two-year colleges surveyed, the mean enrollment was 5,175 with a standard deviation of 786. Test the student's claim at the 0.1 significance level. Preliminary: Is it safe to assume that n4yr≤5% of all students enrolled at a 4-year college in the Unites States and n2yr≤5% of all enrolled at a

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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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 6,288 with a standard deviation of 585. Of the 35 two-year colleges surveyed, the mean enrollment was 5,175 with a standard deviation of 786. Test the student's claim at the 0.1 significance level.

Preliminary:

  1. Is it safe to assume that

    n4yr≤5% of all students enrolled at a 4-year college in the Unites States and
    n2yr≤5% of all enrolled at a 2-year college in the Unites States?

    • Yes
    • No


  2. Is n4yr≥30 and n2yr≥30  ?
    • No
    • Yes
     

Test the claim:

  1. Determine the null and alternative hypotheses. 

    H0: μ4yr      μ2yr 
    Ha: μ4yr      μ2yr 

  2. Determine the test statistic. Round to four decimal places.
    t=

  3. Find the pp-value. Round to 4 decimals.
    p-value = 

  4. Make a decision.
    • Reject the null hypothesis.
    • Fail to reject the null hypothesis.


  5. Write the conclusion.
    • There is sufficient evidence to support the claim that enrollement is higher at a four-year college than a two-year college.
    • 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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