Question

Administrators at a state University want to evaluate whether or not their applicants are substantially different from those of the general population on the GRE (u = 1000, Std dev = 100). A sample of 50 applicants yields an average GRE score of 1035 with a standard deviation of 98.5. Conduct a hypothesis test using alpha = .05 (rejection criterion). When determining the probability value for the study, pay close attention to whether this a one or two tailed hypothesis test.

Step 1: State the hypotheses

Step 2: State your criteria for evaluating the null hypothesis.

Step 3: Compute the test statistic and probability values.

Step 4: Evaluate the null hypothesis

From the results of this study, what can be concluded about the applicants at the state school?

THANK YOU IN ADVANCE!

Answer 1

Solution:

   We are given that: Administrators at a state University want to evaluate whether or not their applicants are substantially different from those of the general population on the GRE (u = 1000, Std dev = 100).

That is: Mean =     and Standard Deviation =

Sample size = n = 50

Sample mean =

Sample Standard Deviation = s = 98.5

Level of significance =

Step 1: State the hypotheses H0 and H1:

Since we have to test Administrators at a state University want to evaluate whether or not their applicants are substantially different from those of the general population on the GRE, which is non-directional and hence we use two tailed test.

Thus H0 and H1 are:

Vs

Step 2: State your criteria for evaluating the null hypothesis.

Since sample size n = 50 > 30 and population standard deviation is known , we use one z test for mean.

Step 3: Compute the test statistic and probability values.

z test statistic:

probability value:

p-value = 2 x P( Z > 2.47 )

p-value = 2 x [ 1 - P( Z < 2.47) ]

Look in z table for z= 2.4 and 0.07 and find area.

P( Z < 2.47 ) = 0.9932

Thus

p-value = 2 x [ 1 - P( Z < 2.47) ]

p-value = 2 x [ 1 - 0.9932 ]

p-value = 2 x 0.0068

p-value = 0.0136

Thus probability value = 0.0136

Step 4: Evaluate the null hypothesis

Rejection Rule: Reject H0, if p-value < 0.05 level of significance , otherwise we fail to reject H0.

Since p-value = 0.0136 < 0.05 level of significance , we reject H0.

Conclusion: Since we have rejected null hypothesis H0, we conclude that there is sufficient evidence to support Administrators claim that their university applicants are substantially different from those of the general population on the GRE.