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 55 such students, the score on the second try was, on average, 34 points above the first try with a standard deviation of 15 points. Test the claim that retaking the SAT increases the score on average by more than 30 points. Test this claim at the 0.10 significance level.

(a) The claim is that the mean difference is greater than 30 (μ_d > 30), what type of test is this?

This is a right-tailed test.

This is a two-tailed test.    

This is a left-tailed test.
(b) What is the test statistic? Round your answer to 2 decimal places.
t_d =  

(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 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 30 points.

There is not enough data to support the claim that retaking the SAT increases the score on average by more than 30 points.    

We reject the claim that retaking the SAT increases the score on average by more than 30 points.

We have proven that retaking the SAT increases the score on average by more than 30 points.

Answer 1

a)

This is a right-tailed test

b)

test statistic td =1.98

c) P-value = 0.0264 (try 0.0265 if this comes wrong)

d )reject H₀

e) The data supports the claim that retaking the SAT increases the score on average by more than 30 points.