Question

In: Statistics and Probability

Two different professors teach an introductory statistics course. The table shows the distribution of final grades...

Two different professors teach an introductory statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader. Answer parts a) and b) below.

Prof. Alpha Prof. Beta
A 5 10
B 12 12
C 15 8
Below C 13 3

a) Find the expected counts for each cell in this table. (Round to two decimal places as needed.)

Prof. Alpha Prof. Beta

A (blank) (blank)

B (blank) (blank)

C (blank) (blank)

Below C (blank) (blank)

b) Test the hypothesis about the two professors, and state an appropriate conclusion. (Assume a significance level of alpha = 0.05) State the appropriate null and alternative hypotheses.

Choose the correct answer below.

A. Upper H 0 : The grade distribution is the same for both professors. Upper H Subscript Upper A Baseline : Professor Alpha gives out more A's than Professor Beta.

B. Upper H 0 : The grade distribution is the same for both professors. Upper H Subscript Upper A Baseline : Professor Beta gives out more C's than Professor Alpha.

C. Upper H 0 : The grade distribution is the same for both professors. Upper H Subscript Upper A Baseline : The grade distributions are different.

D. Upper H 0 : The grade distributions are different. Upper H Subscript Upper A Baseline : The grade distribution is the same for both professors.

- Compute the chi-square statistic. chi squared = (blank) (Round to two decimal places as needed.)

- Find the P-value. The P-value = (blank). (Round to three decimal places as needed.)

- Based on these results, what is your conclusion? Choose the correct answer below.

A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the professors' grade distributions are not equal.

B. Reject the null hypothesis. There is sufficient evidence to support the claim that the professors' grade distributions are not equal.

C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the professors' grade distributions are not equal.

D. Reject the null hypothesis. There is not sufficient evidence to support the claim that the professors' grade distributions are not equal.

Expert Solution

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orchestra answered 1 year ago

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