Question

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

Answer 1

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)