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Chapter 13, numbers 13.8 and 13.10

13.8 Assume that, on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes.

(a) Use t to test the null hypothesis at the .05 level of significance

(b) If appropriate (because the null hypothesis has been rejected), construct a 95 per-cent confidence interval and interpret this interval

13.10 Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance.

(a) Is the true level of significance larger or smaller than .05

(b) Is the true critical value larger or smaller than that for the critical z?

Chapter 14, numbers 14.11 and 14.12

14.11. 14.11 To test compliance with authority, a classical experiment in social psychology requires subjects to administer increasingly painful electric shocks to seemingly helpless victims who agonize in an adjacent room.* Each subject earns a score between 0 and 30, depending on the point at which the subject refuses to comply with authority—an investigator, dressed in a white lab coat, who orders the administration of increasingly intense shocks. A score of 0 signifies the subject's unwillingness to comply at the very outset, and a score of 30 signifies the subject's willingness to comply completely with the experimenter's orders. Ignore the very real ethical issues raised by this type of experiment and assume that you want to study the effect of a "committee atmosphere" on compliance with authority. In one condition, shocks are administered only after an affirmative decision by the committee, consisting of one real subject and two associates of the investigator, who act as subjects but, in fact, merely go along with the decision of the real subject. In the other condition, shocks are administered only after an affirmative decision by a solitary real subject. A total of 12 subjects are randomly assigned, in equal numbers, to the committee condition (X1) and to the solitary condition (X2). A compliance score is obtained for each subject. Use t to test the null hypothesis at the .05 level of significance.

14.11 To test compliance with authority, a classical experiment in social psychology requires subjects to administer increasingly painful electric shocks to seemingly helpless victims who agonize in an adjacent room.* Each subject earns a score between 0 and 30, depending on the point at which the subject refuses to comply with authority—an investigator, dressed in a white lab coat, who orders the administration of increasingly intense shocks. A score of 0 signifies the subject'sunwillingness to comply at the very outset, and a score of 30 signifies the subject'swillingness to comply completely with the experimenter's orders. Ignore the very real ethical issues raised by this type of experiment, and assume that you want to study the effect of a "committee atmosphere" on compliance with authority. In one condition, shocks are administered only after an affirmative decisionby the committee, consisting of one real subject and two associates of the investiga-tor, who act as subjects but, in fact, merely go along with the decision of the real subject. In the other condition, shocks are administered only after an affirmativedecision by a solitary real subject. A total of 12 subjects are randomly assigned, in equal numbers, to the committee condition (X1) and to the solitary condition (X2). A compliance score is obtained for each subject. Use t to test the null hypothesis at the .05 level of significance

__COMPLIANCE SCORES__

**COMMITTEE** **SOLITARY**

2 3

5 8

20 7

15 10

4 14

10 0

14.12 To determine whether training in a series of workshops on creative thinking increases IQ scores, a total of 70 students are randomly divided into treatment and control groups of 35 each. After two months of training, the sample mean IQ 1X for the treatment group equals 110, and the sample mean IQ 2X for the control group equals 108. The estimated standard error equals 1.80.

(a) Using t, test the null hypothesis at the .01 level of significance

(b) If appropriate (because the null hypothesis has been rejected), estimate the stan-dardized effect size, construct a 99 percent confidence interval for the true population mean difference, and interpret these estimates.

Chapter 15, numbers 15.11 and 15.12

15.11 A researcher randomly assigns college freshmen to either of two experimental conditions. Because both groups consist of college freshmen, someone claims that it is appropriate to use a t test for the two related samples. Com

15.12 Although the samples are actually related, an investigator ignores this fact in the statistical analysis and uses a t test for two independent samples. How will this mistake affect the probability of a type II error?

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