**(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.