Chapter 9 Exercises
Prerequisites
prerequisites
Selected answers
You may want to use the Binomial Calculator for some of these exercises.
1. An experiment is conducted to test the claim that James Bond can taste the
difference between a Martini that is shaken and one that is stirred. What is the
null hypothesis?
(Ch. 9.A)
2. The following explanation is incorrect. What three words should be added to make
it correct? (Ch. 9.A)
The probability value is the probability of obtaining a statistic as different from the parameter specified in the null hypothesis as the statistic obtained in the experiment. The probability value is computed assuming that the null hypothesis is true.
3. Why do experimenters test hypotheses they think are false? (Ch. 9.F)
4. State the null hypothesis for:
(a) An experiment testing whether echinacea decreases the length of colds.
(b) A correlational study on the relationship between brain size and intelligence.
(c) An investigation of whether a selfproclaimed psychic can predict the outcome of a coin flip.
(d) A study comparing a drug with a placebo on the amount of pain relief. (A onetailed test was used.)
(Ch. 9.A & Ch. 9.D)
5. Assume the null hypothesis is that µ = 50 and that the graph shown below is the sampling distribution of the mean (M). Would a sample value of M= 60 be significant in a twotailed test at the .05 level? Roughly what value of M would be needed to be significant? (Ch. 9.D & Ch. 6.C)
6. A researcher develops a new theory that predicts that vegetarians will have more
of a particular vitamin in their blood than nonvegetarians. An experiment is
conducted and vegetarians do have more of the vitamin, but the difference is not
significant. The probability value is 0.13. Should the experimenter's confidence
in the theory increase, decrease, or stay the same?
(Ch. 9.F)
7. A researcher hypothesizes that the lowering in cholesterol associated with
weight loss is really due to exercise. To test this, the researcher carefully
controls for exercise while comparing the cholesterol levels of a group of
subjects who lose weight by dieting with a control group that does not diet. The
difference between groups in cholesterol is not significant. Can the researcher
claim that weight loss has no effect? (Ch. 9.F)
8. A significance test is performed and p = .20. Why can't the experimenter claim
that the probability that the null hypothesis is true is .20? (Ch. 9.A, Ch. 9.F & Ch. 9.H)
9. For a drug to be approved by the FDA, the drug must be shown to be safe and
effective. If the drug is significantly more effective than a placebo, then the
drug is deemed effective. What do you know about the effectiveness of a drug
once it has been approved by the FDA (assuming that there has not been a Type I
error)? (Ch. 9.E)
10. When is it valid to use a onetailed test? What is the advantage of a onetailed
test? Give an example of a null hypothesis that would be tested by a onetailed
test. (Ch. 9.D)
11. Distinguish between probability value and significance level. (Ch. 9.B)
12. Suppose a study was conducted on the effectiveness of a class on "How to take tests." The SAT scores of an experimental group and a control group were compared. (There were 100 subjects in each group.) The mean score of the experimental group was 503 and the mean score of the control group was 499. The difference between means was found to be significant, p = .037. What do you conclude about the effectiveness of the class? (Ch. 9.B & Ch. 9.E)
13. Is it more conservative to use an alpha level of .01 or an alpha level of .05? Would beta be
higher for an alpha of .05 or for an alpha of .01? (Ch. 9.C)
14. Why is "Ho: "M1 = M2" not a proper null hypothesis? (Ch. 9.A)
15. An experimenter expects an effect to come out in a certain direction. Is this
sufficient basis for using a onetailed test? Why or why not? (Ch. 9.D)
16. How do the Type I and Type II error rates of onetailed and twotailed tests
differ? (Ch. 9.C & Ch. 9.D)
17. A twotailed probability is .03. What is the onetailed probability if the
effect were in the specified direction? What would it be if the effect were in
the other direction? (Ch. 9.D)
18. You choose an alpha level of .01 and then analyze your data. (a) What is the probability that you will make a Type I error given that the null hypothesis is true? (b) What is the probability that you will make a Type I error given that the null hypothesis is false? (Ch. 9.C)
19. You are playing a game at a carnival. You have to draw one of four cards, and the person running the game claims you have a 1/4 chance of winning. You think that people win the the game less often that this, so you decide to test your hypothesis. You watch many people play the game, and you only see 2 people out of 20 win. (a) Assuming that the probability of winning really is .25, what is the probability of this few people or fewer winning? (b) Can you reject the null hypothesis at the .05 level? (Ch. 9.D)
20. You believe that a coin a magician uses is biased, but you are not sure if it will come up heads or tails more often. You watch the magician flip the coin and record what percentage of the time the coin comes up heads. (a) Is this a onetailed or twotailed test? (b) Assuming that the coin is fair, what is the probability that out of 30 flips, it would come up one side 23 or more times? (c) Can you reject the null hypothesis at the .05 level? What about at the .01 level? (Ch. 9.D)
21. Why doesn't it make sense to test the hypothesis that the sample mean is 42? (Ch. 9.A & Ch. 9.F)
22. True/false: It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level. (Ch. 9.B & Ch. 9.C)
23. True/false: You are more likely to make a Type I error when using a small sample than when using a large sample. (Ch. 9.C)
24. True/false: You accept the alternative hypothesis when you reject the null hypothesis. (Ch. 9.E)
25. True/false: You do not accept the null hypothesis when you fail to reject it. (Ch. 9.F)
26. True/false: A researcher risks making a Type I error any time the null hypothesis is rejected. (Ch. 9.C)
Questions from Case Studies:
Directions: For the following problems (#2730), complete the three parts listed below:
(a)
What is the 95% confidence interval on the difference between means? (Ch. 8.D.5)
(b)
Based on your confidence interval, can you reject the null hypothesis at the .05 level? (Ch. 9.I)
(c)
What do you conclude? (Ch. 9.E & Ch. 9.F)
The following questions use data from the Angry Moods (AM) case study.
27. (AM#6) Is there a difference in how much males and females use aggressive behavior to improve an angry mood? For the "AngerOut" scores, compare the means for each gender.
28. (AM#10) Compare athletes and nonathletes on the mean AngerIn score.
29. (AM#13) Compare athletes and nonathletes on the mean ControlOut score.
The following question uses data from the Teacher Ratings (TR) case study.
30. (TR#7) Compare the difference in ratings between the charismatic and punitive teachers.
Answers:
18) (a) .01
19) (a) .0913
27) (a) (1.16, 2.76)
28) (a) (4.99, .60)
