Many high school students take the SAT\'s twice; once in their Junior year and o

Question

Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 45 such students, the score on the second try was, on average, 30 points above the first try with a standard deviation of 14 points. Test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.10 significance level.

(a) The claim is that the mean difference is greater than 25 (d > 25), what type of test is this?

This is a left-tailed test.This is a two-tailed test.    This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
td =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H0fail to reject H0    

(e) Choose the appropriate concluding statement.

The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points.    

We reject the claim that retaking the SAT increases the score on average by more than 25 points.

We have proven that retaking the SAT increases the score on average by more than 25 points.

Explanation / Answer

Claim : To test whether the mean difference is greater than 25 or not.

Hypothesis : Ho : d < 25 v/s d > 25

Right tailed test . .

By using minitab we can compute this test as ,

Clixk on Stat ---> Basic Stat --------> Paired t ----------> Summarised data differences ---------> sample size = 45 ---------> mean = 30--------> Standard deviation = 14 ---------> Confidence level = 0.90 ------> Test mean : 0 ------> alternative : not equal -------> OK

we get the output of the test as ,

Paired T-Test and CI

N Mean StDev SE Mean
Difference 45 30.0000 14.0000 2.0870

99% lower bound for mean difference: 24.9617
T-Test of mean difference = 0 (vs > 0): T-Value = 14.37 P-Value = 0.000

from output ,

B ) test statistic = 14.37

C ) pvalue = 0.000

D ) Decesion rule : Pvalue < alpha so we reject Ho

The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

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