Question

A test prep website claims that students who use their service improve their SAT scores by more than 109 points. After using the site, a random sample of 25 students improved by an average of 102 points with a standard deviation of 23.2 points.

Answer 1

Here we have to test that

Nul hypothesis :

Alternative hylothesis :

where

This hypothesis test is right tailed test.

n = sample size = 25

Sample mean =

Sample standard deviation = s = 23.2

Here population standard deviation is not known so we use t test.

Test statistic :

t = 1.509 (Round to 3 decimal)

Test statistic = t = 1.509

Consider level of significance = = 0.05

Degrees of freedom = n - 1 = 25 - 1 = 24

Test is right tailed test.

t critical value for = 0.05 and df = 24 is

tc = 1.711 (From statistical table of t values)

Here test statistic < tc

So we fail to reject H0.

Conclusion : There is not sufficient evidence to support the claim that  students who use their service improve their SAT scores by more than 109 points