Question

Researchers collected a simple random sample of the times that it took 81 college students to earn their bachelor’s degrees. The sample mean was 4.8 years with a standard deviation of 2.2 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

Hypothesis -

H0: <= 4.5

Ha: > 4.5

Test statistics

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

= 4.8 - 4.5 / (2.2 / sqrt(81) )

= 1.23

This is test statistics value.

Decision rule-

df = n - 1 = 81 - 1 = 80

From T table,

t critical value at 0.05 level with 80 df = 1.664

Decision rule - reject H0 if test statistics t > 1.664

Decision -

Since test statistics value < 1.664 , we do not have sufficient evidence to reject H0.

p-value-

From T table, with test statistics 1.23 and df 80,

p-value (one tailed) = 0.1112

Conclusion-

We conclude at 0.05 level that we fail to support the claim that mean time for college students to complete their

bachelor's degrees is more than 4.5 years.