(1)The frequency distribution shows the results of 200 test scores. Are the test scores normally​ distributed? Use (alpha) α = 0.10 Complete parts​ (a) through​ (d).Class Boundaries, Frequency

(1)The frequency distribution shows the results of 200 test scores. Are the test scores normally​ distributed? Use (alpha) α = 0.10 Complete parts​ (a) through​ (d).

Class Boundaries, Frequency f.

49.5 - 58.5, 20.

58.5 - 67.5, 61.

67.5 - 76.5, 82.

76.5 - 85.5, 33.

85.5 - 94.5, 4.

Using a​ chi-square goodness-of-fit​ test, you can​ decide, with some degree of​ certainty, whether a variable is normally distributed. In all​ chi-square tests for​ normality, the null and alternative hypotheses are as follows.

H0: The test scores have a normal distribution.

Ha​: The test scores do not have a normal distribution.

a. Find the expected frequencies.

b. Determine the critical​ value, χ20, and the rejection region.

c. Calculate the test statistic.

d. Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim

(2) The table below shows a sample of waiting times​ (in days) for a heart transplant for two age groups. At (alpha) α =​ 0.05, can you conclude that the variances of the waiting times differ between the two age​ groups?

            18-34                                                           35-49

157, 171, 166, 167, 160.                    215, 190, 210, 209, 195, 211, 198.

​(a) Determine the hypotheses. Let σ2/1 be the variance for the​ 18-34 group and let σ2/2 be the variance for the​ 35-49 group.

(b) Determine the critical value.

Calculate the degrees of freedom.

(c) Compute the F test statistic.

(d) Reach a decision.