Question

Test the claim that the mean GPA of night students is smaller than 2.3 at the 0.025 significance level.

Test the claim that the mean GPA of night students is smaller than 2.3 at the 0.025 significance level The null and alternative hypothesis would be: Ho:2 2.3 Ho:H 2.3 Ho: 2.3 Ho:p 2 0.575 Ho:p 0.575 Ho:p0.575 H1: μ < 2.3 H1: μメ2.3 H1ιμ > 2.3 Hi : p < 0.575 H1: pチ0.575 Hi :p > 0.575 The test is: right-tailed left-tailed two-tailed Based on a sample of 60 people, the sample mean GPA was 2.28 with a standard deviation of 0.07 The test statistic is The p-value is: Based on this we: (to 2 decimals) (to 2 decimals) Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 2.3

H_a : $\mu$ < 2.3

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (2.28 - 2.3) / 0.07 / $\sqrt$ 60

Test statistic = -2.21

P(z < -2.21) = 0.0136

P-value = 0.01

$\alpha$ = 0.025

P-value < $\alpha$

Reject the null hypothesis .