Question

# Test the claim that the mean GPA of night students is significantly different than 2.3 at...

Test the claim that the mean GPA of night students is significantly different than 2.3 at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:p=0.575
H1:p>0.575

H0:μ=2.3
H1:μ≠2.3

H0:p=0.575
H1:p≠0.575

H0:p=0.575
H1:p<0.575

H0:μ=2.3
H1:μ>2.3

H0:μ=2.3
H1:μ<2.3

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 40 people, the sample mean GPA was 2.26 with a standard deviation of 0.04

The test statistic is:______ (to 2 decimals)

The positive critical value is:________ (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

we have to test whether the mean GPA of night students is significantly different than 2.3 . So, it is a two tailed hypothesis

test is a two tailed test because we are testing for differece and difference is always two sided test

Using TI 84 calculator

press stat then tests then TTest

enter the data

x = 2.26

s = 0.04

= 2.3

n = 40

press enter, we get

t statistic = -6.32

t critical = T.INV.2T(alpha,df)

where df = n-1 =40-1 = 39 and alpha = 0.05

so, t critical = 2.02

Reject the null hypothesis (because the t statistic is greater t critical value for two tailed hypothesis, so result is significant)