Question

Math SAT: Suppose the national mean SAT score in mathematics was 505. In a random sample of 40 graduates from Stevens High, the mean SAT score in math was 495, with a standard deviation of 30. Test the claim that the mean SAT score for Stevens High graduates is the same as the national average. Test this claim at the 0.01 significance level.

(a) What type of test is this?

This is a left-tailed test.

This is a right-tailed test.    

This is a two-tailed test.

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

(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.

There is enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.

There is not enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.    

We have proven that the mean math SAT score for Stevens High graduates is the same as the national average.

Answer 1

The statistic software output for this problem is :

(a)

This is a two-tailed test.

(b)

Test statistics = -2.11

(c)

P-value = 0.0415

(d)

fail to reject H₀    

(e)

There is not enough data to justify rejection of the claim that the mean math SAT score for Stevens High graduates is the same as the national average.