Question

The average SAT score for the Mathematics portion of the test is 511. In a recent study of 19 individuals that took the test, the average score on the Mathematics portion was 519.3, with a sample standard deviation of 82.4. If the level of significance is 0.01, test the claim that the average SAT score for the Mathematics portion is greater than 511. Show your work to receive credit.

Answer 1

Solution :

Given that ,

$\mu$ = 511

= 519.3

T

s = 82.4

n = 19

The null and alternative hypothesis is ,

H0 :  $\mu$ = 511

Ha : $\mu$ > 511

This is the right tailed test .

Test statistic = T

= (
T
- $\mu$ ) / s / $\sqrt$ n

= ( 519.3 - 511 ) / 82.4 / $\sqrt$ 19

= 0.44

The test statistic = 0.44

df = n - 1 = 19 - 1 = 18

P-value = 1 - ( t 0.44 , 18 )

= 1 - 0.6674

= 0.3326

P- value = 0.3326

$\alpha$ = 0.01

0.3326 > 0.01

P-value > $\alpha$

Fail to reject the null hypothesis .

There is not sufficient evidence to the test claim .