Please show all work. Follow the steps of a hypothesis testing approach. A North
ID: 3218737 • Letter: P
Question
Please show all work. Follow the steps of a hypothesis testing approach.
A North Carolina university wishes to demonstrate that car ownership is detrimental to academic achievement. A random sample of 100 students who do not own cars was sampled and their mean GPA was 2.68. The population standard deviation of GPAs of students who do not own cars was .70. Then a random sample of 100 students who owned cars was sampled and their mean GPA was 2.55. The population standard deviation of GPAs of students who own cars was .60. At the .05 level of significance can we prove that the mean GPA of students who do not own cars is significantly higher than the GPA of students who own cars?
Explanation / Answer
H0: 1 – 2 0
H1: 1 – 2 > 0
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (100-1)*0.70^2+(100-1)*0.60^2/99+99
=0.4252
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(2.68-2.55)-0/0.4252(1/100+1/100)
=0.13/0.09
=1.44
tCRIT is 1.66 and hence reject the null hypothesis
Since 1.44<1.66, we cannot reject the null hypothesis
Hence, we can prove that the mean GPA of students who do not own cars is significantly higher than the GPA of students who own cars.
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