13.6 It’s well established, we’ll assume, that lab rats require an average of 32 trials in a complex water maze before reaching a learning criterion of three consecutive errorless trials. To determine whether a mildly adverse stimulus has any effect on performance, a sample of seven lab rats were given a mild electrical shock just before each trial.

1. Given that \(\bar{X}\) = 34.89 and s = 3.02, test the null hypothesis with t , using the .05 level of sign ifi cance.
2. Construct a 95 percent con fi dence interval for the true number of trials required to learn the water maze.
3. Interpret this con fi dence interval.

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 sampl e. Results show a sample mean, \(\bar{X} \) , of 88 minutes and a sample standard deviation, s , of 9 minutes.

1. Use t to test the null hypot hesis at the .05 level of signifi cance.
2. If appropriate (because the null hypothesis has been rejected), construct a 95 percen t confi dence interval and interpret this interval.

13.9 In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were

1. the car manufacturer? Why?
2. a vigorous prosecutor for the federal regulatory agency? Why?

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 signi fi cance.

1. Is the true level of signi fi cance larger or smaller than .05?
2. Is the true critical value larger or smaller than that for the critical z?

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 int ense shocks. A score of 0 signifi es the subject’s unwillingness to comply at the very outset, and a score of 30 signifi es 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 ar e administered only after an affi rmative 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 ar e administered only after an affi rmative decision by a solitary real subject. A total of 12 subjects are randomly assigned, in equal numbers, t o the committee condition (X1 ) and to the solitary condition (X 2). A compliance score is obtained for each subject. Use t to test the null hypot hesis at the .05 level of signifi cance. (SEE ATTACHEMENT)

14.12 To determine whether training in a series of workshops on creative think ing 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 ( –X1) for the treatment group equals 110, and the sample mean IQ ( –X2) for the control group equals 108. The estimated standard error equals 1.80.

1. Using t , test the null hypothesis at the .01 level of signi fi cance.
2. If appropriate (because the null hypothesis has been rejected), estimate the standardized effect size, construct a 99 percent con fi dence interval for the true population mean difference, and interpret these estimates.

15.8 A school psychologist wishes to determ ine whether a new antismoking fi lm actually reduces the daily consumption of cigarettes by teenage smokers. The mean daily cigarette consumption is calculated for each of eight teen-age smokers during the month before and the month after the fi lm presen tation, with the following results:

(Note: When deciding on the form o f the alternative hypothesis, H 1, remember that a positive differ ence score (D 5 X 1 2 X 2 ) refl ects a decline in cigarette consumption.) (a) Using t , test the null hypot hesis at the .05 level of signifi cance. (b) Specify the p -value for this test result. (c) If appropriate (because the null hypothesis was reject ed), construct a 95 percent confi dence interval for the true population mean for all difference scores, and use Cohen’s d to obtain a standardized estimate of the effect size. Interpret these results. (d) What might be done to improve the design of this experiment?

15.14 In Table 7.4 on page 173, all ten top hitters in the major league baseball in 2011 had lower batting averages in 2012, supporting regression toward the mean. Treating averages as whole numbers (without decimal points) and subtracting their batting averages for 2012 from those for 2011 (so that positive difference scores support regression toward the mean), we have the following ten difference scores: 14, 39, 61, 60, 13, 21, 50, 93, 16, 61.

1. Test the null hypothesis (that the hypothetical population mean difference equals zero for all sets of top ten hitters over the y ears) at the .05 level of signifi cance.
2. Find the p -value.
3. Construct a 95% confi dence interval.
4. Calculate Cohen’s d .
5. How might these fi ndings be reported?

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