Question

10. Do students who learned English as well as another language simultaneously score worse on the SAT Critical Reading exam than the general population of test takers? The mean score among all test takers on the SAT Critical Reading exam is 501. A random sample of 100 test takers who learned English as well as another language simultaneously had a mean SAT Critical Reading score of 485 with a standard deviation of 116. Do these results suggest that students who learn English as well as another language simultaneously score worse on the SAT Critical Reading exam?

(a) State the appropriate null and alternative hypotheses.

(b) Verify that the requirement to perform the test.

(c) Use p-value approach at α=0.05 to test the hypotheses in part (a).

(d) Write a conclusion based on your results to part (c).

Answer 1

Answer)

A)

Null hypothesis Ho : u = 501

Alternate hypothesis Ha : u < 501

Given N = 100

Sample mean = 485

S.d = 116

B)

As the population s.d is unknown here we will use t table to conduct the test.

C)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

= (485-501)/(116/√100)

= -1.379

Degrees of freedom is = n-1, 100-1, 99

For df 99 and test statistics -1.379

P-value from t table is = 0.085501

As the obtained P-Value is greater than given alpha 0.05

We fail to reject the null hypothesis Ho.

D)

So, we do not have enough evidence to support the claim.