Question

Test the claim that the mean GPA of night students is smaller than 3.2 at the .025 significance level.

Based on a sample of 75 people, the sample mean GPA was 3.18 with a standard deviation of 0.06

The test statistic is (to 3 decimals)

The critical value is (to 3 decimals)

Answer 1

Solution:

Claim:  mean GPA of night students is smaller than 3.2

So hypothesis are

H0: = 3.2

H1: < 3.2

n = 75   ....sample size

= 3.18   ...sample mean

s = 0.06 ....Sample standard deviation

= 0.025 .... level of significance

Since population SD is unknown,we use t test.

The test statistics t is given by ..

t =  

= (3.18 - 3.2)/(0.06/75)

= -2.887

The test statistic is  -2.887

Now, < sign in H1 indicates that the left tailed test.

So, the critical value is   i.e.  

The critical region : t <    

  =   _0.025,74 = 1.993 (using t table)

= -1.993

The critical value is -1.993