Question

1. The provost at the University of Chicago claimed that the entering class this year is larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The University’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Round final answers to two decimal places. Solutions only.

(C) State the null hypothesis for this study.

(D) State the alternative hypothesis for this study.

(E) What critical value should the president use to determine the rejection region?

(H) The lowest level of significance at which the null hypothesis can still be rejected is ___.

Answer 1

C. Here the claim is that mean is less than previous year

As null hypothesis always have equality sign, claim would be alternative hypothesis

So null hypothesis is

D. As mentioned in c clsim is alternative hypothesis

So

E. Now n is small and population variance is not known we will use the distribution.

The t-critical value for a left-tailed test, for a significance level of α=0.05 is

t=−1.729

Graphically

H. Now that statistics is

So we see that for alpha=0.05 t statistics is not in rejection area so we won't reject null hypothesis.

But for alpha=0.10

The t-critical value for a left-tailed test, for a significance level of α=0.10 is

tc=−1.328

Graphically

So answer is 0.10 as for this value the statistics falls in rejection region