Question

DETAILED WORK PLEASE

(1 point) Test the claim that the population of sophomore college students has a mean grade point average of 2.24 versus a mean grade point average greater than 2.24. Sample statistics include n = 15, x = 2.38, and s = 0.5. Use a significance level of a = 0.01. The test statistic is The critical value is The final conclusion is A. There is not sufficient evidence to support the claim that the mean grade point average is greater than 2.24. B. There is sufficient evidence to support the claim that the mean grade point average is greater than 2.24.

Answer 1

Solution :

Given that,

Population mean = $\mu$ = 2.24

Sample mean = $\bar x$ = 2.38

Sample standard deviation = s = 0.5

Sample size = n = 15

Level of significance = $\alpha$ = 0.01

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: $\mu$ $\leq$ 2.24

Ha: $\mu$ 2.24

The test statistics,

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

= ( 2.38 - 2.24 ) / ( 0.5 / $\sqrt{}$ 15 )

= 1.084

Critical value of  the significance level is α = 0.01, and the critical value for a right-tailed test is

$t_{c}$ = 2.624

Since it is observed that t = 1.084 $\leq$ $t_{c}$ = 2.624, it is then concluded that the null hypothesis is fail to rejected.

Conclusion:

A)