Question

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.

Answer 1

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