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

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
icon
Related questions
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:

  1. 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


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

Test the claim:

  1. Determine the null and alternative hypotheses. 

    H0H0: μ4yr      μ2yr 
    HaHa: μ4yr      μ2yr

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

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

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


  5. 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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps with 2 images

Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill