Practice Problems

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Prerequisite topics:

Review exercises suggested in the NSEES Diagnostic Exam. All are from Moore and McCabe.
- Normal distribution: You should read section 1.3 and do review exercises on pages 87-90 in the Moore and McCabe text. Suggested: 1.75, 1.77, 1.85, 1.87, 1.89, 1.93.
- Understanding p-values is crucial for introductory statistics. You should be able to interpret a p-value (as in exercises 6.33) and calculate a p-value (exc. 6.35, 6.37). You should know the difference between one-sided and 2-sided p-values as well (exc. 6.40 vs. 6.41). Also exc. 6.43.
- Confidence intervals: Exc 6.6, 6.13, 6.19, 6.21, 6.23
- It is essential that you understand the sampling distribution of the sample mean and the Central Limit Theorem. Review section 5.2 of Moore and McCabe and do the following exercises: 5.29, 5.33, 5.35, 5.37. Also section 6.1: Exc. 6.1, 6.3, 6.7, 6.9, 6.11.
- You should review one-sided tests in Section 6.2 of Moore and McCabe, particularly pages 455-456. Exercises 6.27 and 6.29 will be of help. You should also know how to do 6.35 and 6.37.
- You should read section 7.1 of Moore and McCabe to make sure you understand the form of the standard error and how it differs from the standard deviation.
- Review the components of a confidence interval -- the standard error, the choice of z or t quantiles and the degrees of freedom if you choose a t. You should know when to use a t versus a z distribution. Review pages 503-517 of Moore and McCabe. Suggested Exercises: 7.1, 7.7, 7.9, 7.11, 7.15.
- The natural logarithm of any number k (in this case, k = x + y) is the exponent which raises the constant e to the number k. It is critical that you know how to do basic calculations with natural logs. Please review this topic in your calculus book because you will see it numerous times in your NSEES career.
- Summary statistics: You should read section 1.2 and 1.3 of Moore and McCabe. Suggested review exercises: 1.95, 1.75, 1.77, 1.85, 1.87, 1.89, 1.93.
- Correlation coefficient: When the correlation coefficient is negative, this means that as variable A increases, variable B decreases; a value close to -1 indicates a strong inverse relationship. A value close to zero indicates a weak relationship. You should read section 2.2. Suggested exercises: 2.22, 2.25, 2.32.
- Analysis of Variance:
  - You should read chapter 12 through p.775. Suggested exercises: 12.9, 12.21, 12.23, 12.25.
All conceptual exercises from Ch 1 and 2 of Sleuth.
Ch 3 of Sleuth, p. 72: Conceptual exercises 1,2,3,4,9,10.
Ch 5 of Sleuth, p. 135-136, Exercises 4, 8, 9, 11, 12, 13, 18

Practice Problems for Quiz 2, covering Chapter 7 and Chapter 8 (except 8.4,8.5)

Review all ANOVA material. Make sure you understand the difference between ANOVA and simple linear regression models.
Chapter 7, all conceptual exercises. Computational exercises: #13, 14. Also #20-23 concern meat processing data. Columns are "time" and "ph". Do problem #20 (run the regression here. For part (c), the regression equation you will enter is "ph~I(time-5)"). #21 (follows on #20). #22 (do graphically and using formula), #23.
Sample problem from past final exam
Spring 2001 midterm (skip problem 10 for now)
For the two monitor problem from lecture, test whether B's measurements are greater than A's by a fixed additive amount (test whether the intercept is nonzero). Test whether the slope is greater than 1 (do measurements at monitor A exceed monitor B by a multiplicative factor greater than 1?).
Chapter 8, Conceptual exercises #2,4,5,6,8,9,10,11,13,14. Make sure you read 8.6.2 and study Display 8.11.
Practice Problems for Midterm, covering Chapters 7 and 8 and lecture material through 2/14
Of course, everything listed previously is fair game for the midterm.
All conceptual exercises from Chapter 7 & 8.
A non-comprehensive list of problems from Moore and McCabe. These problems represent some fundamental concepts in ANOVA and regression and are worth reviewing. In the past, students have found these to be useful for review of more basic concepts.
- Chapter 2. #2.25. #2.30. #2.32. #2.46. #2.66. #2.68. #2.79. #2.110.
- Chapter 10. #10.6 (requires typing in some data and producing simple output). #10.11, 10.12, 10.13, 10.14. #10.20, 10.21. #10.28 (see page 693 for a hint).
- Chapter 11. #11.1, 11.2, 11.3, 11.5-11.11.
- Chapter 12. #12.21, 12.22, 12.23
Breakdown time of insulating fluid. Work through the results in Case Study 2 of Chapter 8. Make sure you can replicate and understand the interpretation of all results in the text. In particular, confirm the conclusions on the bottom of page 207. Go through 8.7 comments.
Meat processing example from class. Use the lecture notes to confirm the results at the top of page 208. And make sure you understand the interpretations.
Island area and number of species. Work through the results in Case Study 1 of Chapter 8. Make sure you can replicate and understand the interpretations in the case study summary, as well as the middle of page 208. Go through 8.7 comments.
Sample problems from a past Statistics 101 course.
Adapted from "Crab claw size and force", #25 Sleuth, page 194, Ch. 7. These data come from: Behrens Yamada, S. and E.G. Boulding. 1998. Claw morphology, prey size selection, and foraging efficiency in generalists and specialist shell-breaking crabs. Journal of Experimental Marine Biology and Ecology 220:191-211. (FYI: It can be easily downloaded from Duke E-Reserves.) Data in crabclaw.txt. Variables: Mean closing force (Newtons) and height (mm). Results for Hemigrapsus nudus are:
Call: lm(formula = log(force) ~ log(height))
Residuals:
Min 1Q Median 3Q Max
-0.5903 -0.2775 -0.082 0.2517 0.8882

Coefficients:
Value Std. Error t value Pr(>|t|)
(Intercept) 0.5191 1.1147 0.4657 0.6497
log(height) 0.4083 0.5426 0.7525 0.4663

Residual standard error: 0.4825 on 12 degrees of freedom
Multiple R-Squared: 0.04506
F-statistic: 0.5662 on 1 and 12 degrees of freedom, the p-value is 0.4663
1. What is the effect of a tripling of the height for the Hemigrapsus nudus? Give a 95% confidence interval for this multiplicative factor in the median. What are the units of b₁? (the slope of the regression line)
2. For each crab, closing forces were measured repeatedly, by measuring the force as the claws pulled two wires together. Could this be considered an ecological regression? Why or why not? Are their any other statistics besides the mean that might be appropriate to measure closing force?
3. Perform a test of whether closing force is an increasing function of height. Give hypotheses, test statistic and conclusion of your test. (Remember, the log transform is an order-preserving transformation. Thus, you can perform a test on the log scale and interpret it on the original scale. Effectively, you are performing a test regarding the multiplicative factor in the median.)
Spring 2001 midterm Problem 10

Chapter 9: All conceptual exercises.

Chapter 10:

If you haven't already, work through all research questions/results for the bat data. Computational exercise #13 is good practice. In 13b, report the confidence intervals for slopes of each of the 3 species and write 1-sentence interpretations of each (use careful language). Under the parallel regression lines model, for *each* of the three species, how would you use the computer centering trick to calculate a prediction interval for the median energy expenditure for a future observation of median body mass=200g? How would you use the computer centering trick to calculate a confidence interval for the median energy expenditure for a median body mass of 200g? How do these intervals differ? How do they change as median body mass is increased to 400g?
All conceptual exercises
Computational exercises: #9, 10, 11

Chapter 11. All conceptual exercises.

Chapter 12. All conceptual exercises. Computational exercises #10, 11 illustrate a few good points, although they are somewhat tedious. #10: Do the calculations for one of the models. #11: Do the first couple of stepwise steps.

Chapter 18 conceptual exercises

Chapter 20 conceptual exercises # 1(a,b), 2,3, 5-8. Computational exercise: #9.

Past exams and quizzes:

Spring 2001 Quiz

Spring 2001 Midterm

Spring 2001 Final Skip #19.