Question

Retaking the SAT: Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 50 such students, the score on the second try was, on average, 28 points above the first try with a standard deviation of 13 points. Test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.01 significance level.

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

This is a two-tailed test.

This is a left-tailed test.

This is a right-tailed test.

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

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

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

reject H0

fail 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.

Answer 1

Solution :

Given that,

Population mean = = 25

Sample mean = = 28

Sample standard deviation = s = 13

Sample size = n = 50

Level of significance = = 0.01

a)

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 25

Ha: 25

b)

The test statistics,

t = ( - )/ (s/)

= ( 28 - 25 ) / ( 13 / 50)

= 1.632

c)

P- Value = 0.0546   

The p-value is p = 0.0546 0.01 it is concluded that the null hypothesis is fails to reject.

d)

fail to reject H0  

e)

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

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