1. Consider the critical flicker frequency data (supplied with this assignment). Test the null hypothesis that the distribution of cff values is the same for all of the eye colors against the general alternative, and report the p-value which results using

1. an ANOVA \(F^{\prime}\) test (see part (f) - you might as well generate the plot while you're doing the test),
2. the Tukey-Kramer test,
3. the Kruskal-Wallis test,
4. the rank analog of the Tukey-Kramer test (give the value of the test statistic in addition to a statement about the p-value),
5. the Steel-Dwass test (give the value of the test statistic in addition to a statement about the p-value).
6. Also give a probit plot of the pooled residuals.

(Don't concern yourself with the fact that one of the sample sizes is less than 6 , although in practice this might something to worry about to a mild degree.)

2) Consider the data (supplied with this assignment) from the experiment to study the gain in weight of rats fed on four different diets.

1. Does the amount of protein affect the mean weight gain? Respond to this query by reporting the \(p\) -value which results from an appropriate \(F\) test.
2. Does the source of protein affect the mean weight gain? Respond to this query by reporting the p-value which results from an appropriate \(F\) test.
3. (Report) Now try to impress me with some additional observations concerning this analysis of variance problem. Give me a two page report (including plots within the two pages) summarizing your findings, being as thorough as possible while observing a two page limit. Highlight your key conclusions. (Hand in this part separately, actually giving me a two page report.)

3) Consider the data (supplied with this assignment.) from the study designed to assess the effects of diet on serum cholesterol level. Does the data provide significant evidence indicating that the choice of diet affects the serum cholesterol level? Respond to this query by reporting the value of the test statistic and the p-value which results from the most appropriate \(F\) test.

4) Consider the detergent data (supplied with this assignment.). Do a nonparametric test of the null hypothesis that the distribution of whiteness readings is the same for all four detergents against the general alternative, and report the p-value accurately.

5) (Report) Suppose that the Army takes four sheets of metal and divides each into five pieces and paints each piece from a sheet a different shade of green (using proper randomization, of course). Further suppose that the reflectivity of each piece is measured twice and that the measurements are as given below.

Does the paint color affect the reflectivity? Say something about the p-value which results from the most appropriate test. Also, make some additional observations concerning this analysis of variance problem. Give me a two page report (including plots within the two pages) summarizing your findings, being as thorough as possible while observing a two page limit. Highlight your key conclusions. (Hand in this part separately, actually giving me a two page report.)

6) Consider the data pertaining to $\mathrm{CHD}$ and tension (supplied with this assignment).

1. Does this data provide statistically significant evidence indicating that people who work under tension are more likely to have a major CHD event than people who do not work under tension? What can be said about the p-value which results from the most appropriate test? (Give the value of the test statistic and make a statement about the $p$-value.)
2. Give a $99 \%$ confidence interval for $p_{y}-p_{n}$, where $p_{y}$ is the probability of someone who works under tension having a major CHD event and $p_{n}$ is the probability of someone who does not work under tension having a major CHD event.

7) Consider the tomato data (supplied with this assignment) from the linkage study. Test the hypothesis that the four phenotypes occur with probabilities \(9 / 16,3 / 16,3 / 16\), and \(1 / 16\) against the general alternative that this is not the case using a likelihood ratio test, and report the p-value. (Note: The null hypothesis corresponds to having the probability of getting a tall plant being \(3 / 4\) and the probability of getting a cut-leaf plant being \(3 / 4\), with the event that a tall plant is obtained being independent of the event that a cut-leaf plant is obtained.)

8) Consider the juvenile delinquent data (supplied with this assignment). Does this data provide statistically significant evidence indicating that delinquents with poor eyesight are less likely to wear glasses than are nondelinquents with poor eyesight? Respond to this query by accurately reporting the p-value which results from the most appropriate test.

9) Consider the flying bomb data (supplied with this assignment). Test the null hypothesis that the data corresponds to iid Poisson random variables against the general alternative that this is not the case using Pearson's chi-square test based on the six categories 0,1,2,3,4, and 5 or more. Use the sample mean as an estimate of the distribution mean and report the \(p\) -value.

10) Subjects were classified by two factors: how much they snored and whether or not they had heart disease. Does the data below provide significant evidence to indicate that the two factors are not independent? Report the p-value (or make a statement about the p-value) which results from an appropriated test.

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