Question

2. The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the studentsthat took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.(For fullcredit need to draw the curve and shade the area)

H0: Test Stat:

H1:

Conclusion:

Answer 1

Let be the mean of MCAT score.

We want ot test   the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5

The null hypothesis will be

I.e mean score is equal to  29.5

vs the alternative hypothesis will be

.i.e mean score greater than 29.5

The sample of 40 students have mean MCAT score of 32.2 with a standard deviation of 4.2.

The sample mean is

and the sample standard deviation

s = 4.2

The test statistic is given as

=   4.065786

Now obtaining the critical value from the t-table

Dicision rule:

Reject H0 if t ( calculated value ) > t( critical value)

i.e

Since

t( calculted value) =4.065786 > t (critical value) =1.6849

We reject the null hypothesis

The shaded region is critical region since this is upper tailed test. Since our test statistic fall in this region , we reject the null hypothesis