Question

In: Statistics and Probability

Students in the senior capstone course (N = 36) at University Uptight took the Political Science...

Students in the senior capstone course (N = 36) at University Uptight took the Political Science subtest developed by the National Bored Testing Association. The test is a 75-item, multiple-choice test covering all areas of political science. The national norms for the test show a mean of 50. The mean for the students in the capstone was 55, with a standard deviation of 15. Did the students at UU score significantly higher than the national norms?

A.State your null and alternative hypotheses.

B.Is this a one- or two-tailed hypothesis? Explain.

C.Calculate the appropriate statistical test.

D.Can you reject the null hypothesis? Why or why not?

E.What is the probability of a Type I error? Type II error?

F.Write a Results section for your findings. Include the descriptive statistics, type of statistical test and results of the test, and effect size.

G.Write a Discussion section for your findings. Include the findings, interpretation/explanation/implication of the findings, and possible next studies.

Expert Solution

A. H0: Mean of UU students is same as national average

H1: Mean of UU students is higher than national average

B. This is a once tailed hypothesis as we are concerned with value greater than 50 (national mean).

C. Sample mean =55

Sample standard deviation = 15

test statistic = (x-50) / (15/ n )

= (55 -50) / (15/36) = 2

this is a t distribution with n-1 that is 35 degrees of freedom.

D. critical value at 0.05 significance is 1.6896

as 1.6896 < 2 we can reject null hypothesis at 0.05 significance.

E. Probability of type 1 error is significance level. It is the probability of rejecting null hypothesis given that it is true.

Type 2 error is not rejecting null hypothesis given that it is false. In our case, we will not reject the null hypothesis given that it is infact 55, when our test statistic is less than 1.6896 . The value at 1.6896 t score is 54.224.

So, if mean is 55 and our value is less than 54.224 we commit a type two error.

t score in this case is : (54.224-55)/ (15/36) = -.3104

probability of this is 0.379

F and G. This is a t-test. Test statistic value is 2. Critical value at 0.05 significance is 1.6896. As our value is greater than this, we reject the null hypothesis.

The probability of type 1 error is : 0.05

Probability of type 2 error is: 0.379

orchestra answered 1 year ago

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