Question

Test the claim that the mean GPA of night students is significantly different than 3 at the 0.02 significance level.

The null and alternative hypothesis would be:

Test the claim that the mean GPA of night studentsis significantly differ ent than 3 at the 0.02 significance level ר o/1) The null and alt ernative hypoth esis would be: о/3) Hp0.75 H 3 Hp 0.75 H: 3 H 3 H: p 0.75 H p0.75 H: u3 Hi:p 0.75 Hi:3 H:3 Hp < 0.75 0/3) o/5) 0/5) D/2) The test is o/1) two-tailed left-tailed right-t ailed o/2) К0/1) К0/4) (0/4) Based on a sample of 40 people, the sample mean GPA was 2.98 with a stan dard deviation of 0.04 (0/4) (0/4) К0/4) The test statistic is (to 3 decimals) The positive critical value is (to 3 decimals) (0/4) К0/4) К0/4) К0/6) (0/4) К0/2) Based on this we O fail to reject the null hypothesis Oreject the null hypothesis License Points possib le: 4 89 Unlimited attempts

Answer 1

Solution :

Given that,

Population mean = $\mu$ = 3

Sample mean = $\bar x$ = 2.98

Sample standard deviation = s = 0.04

Sample size = n = 40

Level of significance = $\alpha$ = 0.02

This is a two tailed test.

The null and alternative hypothesis is,

Ho: $\mu$ $=$ 3

Ha: $\mu$ $\neq$ 3

The test statistics,

t = ( $\bar x$ - $\mu$ )/ (s/$\sqrt{n}$)

= ( 2.98 - 3 ) / ( 0.04 / $\sqrt{}$ 40 )

= -3.162

Critical value of  the significance level is α = 0.02, and the critical value for a two-tailed test is

$t_{c}$ = 2.426

Since it is observed that |t| = 3.162 > $t_{c}$ = 2.426 , it is then concluded that the null hypothesis is rejected.

Reject the null hypothesis.