I have not consulted any human sources for this exam. Name:___________________________

For each situation, pick the letter that gives the best description of the proper analysis.

1. __ A researcher collects the average wing lengths and body lengths of 24 species of warblers. After taking logs (of course!) she wants to check for a linear relationship.

2. __ The researcher has collected carapace width and pincer strength for 24 lobsters in each of two species. She wants to know whether, after allowing for carapace width, pincer strength differs in the two species.

3. __ A researcher measured the speed of movement, length, weight, and circumference of 46 snakes, to investigate whether speed of movement is related length, weight, and circumference.

4. __ Twenty-seven containers were prepared, nine at each of three salinity levels. The % weight gain was recorded for a blue crab in each container. Does growth rate depend on salinity level?

5. __ In 1998, Heron Island had 78 black noddy nests on the west side, of which 8 were not successful. On the east side, there were 102 nests, and 7 were not successful. How does the researcher check for a relationship between side of island and nesting failure?

6. __ The growth rate of bacteria in cultures was studied by growing eight cultures at 20^o C and eight at 25^o C. Half of the eight at each temperature were made up as enriched medium and half as the standard medium.

A. Correlation coefficient E. Contingency table

B. Randomized block design F. Two-factor factorial design

C. Completely randomized design G. ANCOVA

D. Linear regression H. Multiple regression

In the following multiple-choice problems, circle every letter which applies (could be none.)

7. Concerning the test of independence in a contingency table

1. The expected frequencies are calculated assuming row and column classifications are independent.
2. If the null hypothesis is rejected, there is sufficient evidence to conclude the row and column classifications are related.
3. The chi-squared distribution is an approximation to the distribution of the test statistic
4. If the null hypothesis is rejected, there is sufficient evidence to conclude that the row and column classifications are dependent.

8. Concerning designed experiments,

1. Blocking permits comparison of treatments on similar experimental units.
2. They have an advantage because they are more realistic than observational studies.
3. Randomly assigning experimental units to treatments increases the variability of errors.
4. Violation of normally distributed errors has little effect on the F test.

9. Concerning multiple regression (assume correlated predictor variables)

1. When a variable is added to the regression, R² will never decrease.
2. The t ratio for a variable depends on which other variables are in the model.
3. When there are many predictors, several models could fit the data equally well.
4. The partial F test for a coefficient is based on assuming that variable is the last variable added to the model.

10. Concerning checking assumptions

a) Residuals vs. order of observations should be used to check for independence of errors.

2. It is most important to avoid concluding an assumption is violated when it is satisfied.
3. Residuals vs. fits plots might reveal that errors do not have mean zero.
4. Normal plots of predictors are useful to check for outliers in the errors.

11. Concerning C_p plots

1. C_p estimates the mean-squared error of the residuals
2. The plot will usually identify the best model.
3. If two models have the same C_p , the one with the most predictors is estimated to have smaller prediction variance.

d) The better models are to be found closest to the line C_p = p.

12. The F ratio was 2.71, with d.f. = 2 and 16.

1. Give the lowest p-value you can, according to the F tables in your text (State text used.)
2. If this F is for a test of H₀: b ₁ = b ₂ = 0 in a multiple regression containing two predictors, give the appropriate conclusion in words.
3. If a partial F test for testing H₀: b ₂ = 0 in the same regression was 5.26 with d.f. = 1, 16, give the best p-value, according to the tables in your text.
4. Give the appropriate conclusion to c) in words.

13. The effects of different diets on weight gain were compared in a randomized block design. Each block consisted of four pigs from the same litter; each pig on a different diet.

1. Describe, in words pertaining to this experiment, what a treatment-block interaction is.

b) If the residual vs. fits plot showed a pattern like a bowl, what would you do?