Question

Researchers collected a simple random sample of the times that it took 212 college students to earn their bachelor’s degrees. The sample mean was 4.72 years with a standard deviation of 1.95 years. (National Center for Education Statistics, 2008) Use a significance level of 0.05 to test the claim that the mean time for college students to complete their bachelor’s degrees is more than 4.5 years.

Answer 1

H0:   <= 4.5

Ha: > 4.5

This is right tailed test.

Test statistics

t = ( - ) / ( S / sqrt ( n) )

= ( 4.72 - 4.5) / (1.95 / sqrt ( 212) )

= 1.64

df = n - 1 = 212 - 1 = 211

From T table, critical value at 0.05 significance level with 211 df = 1.652

Since test statistics < 1.652 , fail to reject H0.

We conclude that , we fail to support the claim that the mean time for college students to complete

their bachelor’s degrees is more than 4.5 years.