(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?
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.