Question

The current widely held belief is that there is no difference in much people make whether they get a four-year bachelor’s degree or they first attend community college and then transfer to a college/university to finish their bachelor's degree. However, a recent report claims people with a four-year bachelor’s degree earn more than people who transfer from a community college and then finish their bachelor’s degree. To test the validity of this new claim, a sample of 150 people with a 4-year degree was collected and the sample mean salary was $54,700. A sample of 100 people who transferred from a community college was taken and the sample mean salary was $52,000. Perform the hypothesis test of the difference of the 2 population means with α = 0.05 testing the claim that people with a four-year bachelor’s degree earn more than people who transfer from a community college. Assume the POPULATION STANDARD DEVIATION is $4,000 for four-year degrees and $1,500 for community college transfers.

1- The value of the Test Statistic for this hypothesis test is ? (rounded to 2 decimal places)

2-The Critical Value for the hypothesis test is ?

Answer 1

let

4 year degree sample is sample 1

so for this sample we have following data

sample size =n1=150 mean salary=m1=54700 SD1=4000

let community class transfers is sample 2

sample size =n2=100 mean salary =m2=52000 SD2=1500

we have to test that if people with a four-year bachelor’s degree earn more than people who transfer from a community college

Hence

a)

now test statistics is given by

b)

test is right tailed test so

critical value is given by

P(Z> critical value ) =0.05

from Z table P(Z>1.645)=0.05

hence critical value =1.645

we reject H0 if Z>1.645

c)

since Z calculated in part (a) is greater than the critical value given in part (b) so we reject H0 Hence there is enough evidence to conclude that people with a four-year bachelor’s degree earn more than people who transfer from a community college.