STA 3024 Test 3 Spring, 2001 Due: Wednesday April 25, 9 A.M.

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. ___ The researcher has collected head width and body weight for 45 ants. She wants to know whether the two variables have a linear relationship.
  2. ___ The % successful nests, % ground cover, and degree-days (total temperature) during nesting were measured for 36 plots in a wildlife sanctuary. The researcher wants to be able to predict % successful nests using ground cover and degree days.
  3. ___ In the Apalacicola National Forest, 100 plots were sampled; 48 of them had been logged in 1985, and 52 had not. Ten of the logged plots contained red-cockaded woodpecker nests, while 25 of the unlogged plots had nests. Are logging and presence of nests associated?

4. ____ A researcher measured time to exhaustion for fish in a test tank. She tested them using water temperature of either15o or 20o C, and current speed of either 0.25 or 0.75 m/sec. There were six fish under each condition, 24 in all. The researcher wants to see whether time to exhaustion is related to current speed or water temperature.

  1. ___ Ten stone crabs were selected from each of the four areas. The researcher wanted to compare the weight of the crabs in different areas.

6. ___ The researcher has measured number of species and % understory on 20 plots in each of two nature preserves. She wants to know whether number of species differs in the two preserves, if % understory is taken into account.

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 goodness-of-fit tests

  1. The true distribution of the test statistic is only approximately chi-squared.
  2. Expected frequencies should always be greater than five
  3. The test shouldn't be used on continuous data unless it is grouped into intervals.
  4. If the null hypothesis is rejected, it is valid to conclude that the assumed distribution does not fit the data.

8. Concerning designed experiments

  1. Conditions may be less realistic than in observational studies.
  2. You can do experiments on human subjects that would be unethical in observational studies.
  3. Randomization of treatments to experimental units helps counter objections that the results are due to some uncontrolled factor.
  4. When the errors are correlated the F test for equal means is untrustworthy.

9. Concerning multiple regression, assuming the predictors are correlated,

  1. When a variable is deleted from the regression, SSreg will never increase.
  2. Adding a variable to the model will change the other coefficients.
  3. The SSreg for a variable depends on which other variables are in the model.
  4. The partial F test for a coefficient is the square of Minitab's t ratio for that variable..
  1. Concerning checking assumptions with plots
  1. Plots are more useful than formal tests because they are more objective.
  2. Normal scores plots of residuals are not useful for checking for constant variance of errors.
  3. Residuals vs. fits plots are useful for checking whether errors are correlated over time.
  4. Normal plots of predictors are used to detect skewness and outliers in the predictors.
  1. A researcher used body weight x in kg to predict calorie consumption y while performing a standard exercise for men and women. The prediction equation was y-hat = 84 + 4x +27D, with D = 1 for men, 0 for women.
  1. Describe the relationship between y and x for women.
  2. Describe how men and women differ on calorie consumption, taking into account body weight.
  3. State why (or why not) ANCOVA can be used in this problem.

12. The F ratio was 6.60, with d.f. = 3 and 10.

  1. Give the smallest p-value you can, according to the F tables in your text.
  2. If this F is for a test of H0: b 1 = b 2 = b 3 = 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 of y on x1, x2, x3 was 5.01 with d.f. = 1, 10, give the smallest p-value, according to the tables in your text.
  4. Give the appropriate conclusion to c) in words.

A two-factor completely randomized factorial design was used to investigate the effect of nest shading (Yes, No) and Ground Cover (High, Low) on nestling growth.

  1. Describe, in words pertaining to this experiment, what an interaction is.
  2. Draw an interaction plot that shows that the nest shading has a negative effect on nestling growth when Ground Cover is high, but no effect when Ground Cover is low.