Part I

Part I. Multiple Choice. Please write your answers in the blue book or clearly circle them on this page.

1. A type I error occurs when we:

a) fail to reject a true null hypothesis c) reject a true null hypothesis

b) fail to reject a false null hypothesis d) reject a false null hypothesis

2. When is the t statistic used for hypothesis testing instead of the z statistic?

a) When the sample size is n=30 or larger

b) When the mean of the population is unknown

c) When the standard deviation of the population is unknown

d) When you are not sure if the population distribution is normal

3. An important assumption for hypothesis testing with z-scores is that:

a) large alpha levels must be used c) random assignment is used

b) the sampling distribution of the mean is normal d) all of the above

4. Which of the following statements about the t statistic is FALSE?

a) The t distribution is actually a family of distributions, one for every sample size

b) As the estimated standard error decreases, the value of the t statistic decreases

c) As the sample size increases, the t distribution appears more and more like the z-distribution

d) As the sample size increases, the degrees of freedom increase

5. Which of the following statements about independent samples hypothesis testing is FALSE?

a) The null hypothesis states that there is no difference between the population means

b) When pooling sample variances, the resulting value will be closer to the variance of the smaller sample

c) When the actual difference between the sample means is greater than that expected by chance, the null hypothesis will

most likely be rejected

d) The variance of the two populations must be approximately equal to use an independent samples t-test

6. Compared to the estimated standard error for two independent samples, the standard error for two related samples will be:

a) the same b) larger c) smaller d) more variable

7. If the null hypothesis is true, what value should you expect for any t-statistic?

a) 0 b) 1.00 c) -1.00 d) 1.65

8. If we increase our level of confidence, say from 95% to 99%, we will obtain a ______.

a) narrower, more precise confidence interval c) wider, more precise confidence interval

b) narrower, less precise confidence interval d) wider, less precise confidence interval

9. The probability of correctly rejecting a false null hypothesis is equal to:

a) a b) b c) 1- b d) 1 - a

10. The Burpo Beer company is considering launching new flavored beers and would like you to design a study to determine whether people would prefer fruit flavored beer or chocolate flavored beer. The company is particularly interested in minimizing individual differences in taste preferences, which are known to be quite large. Given this consideration, which of the following research designs would be most appropriate?

a) single sample design c) repeated measures design with counterbalancing

b) independent samples design d) repeated measures design without counterbalancing

Part II. Short Answer & Computational Questions. Please write all responses in the blue book. Clearly show all work. Failure to show all work will result in loss of credit. Carry calculations to four decimal places and final answers to two decimal places.

(1) List three things a researcher can do to increase the power of a study.

(2) Most psychologists would have more confidence in the findings of a study in which the null was rejected with a = 0.05 and n = 50 than a study in which the null was rejected with a = 0.05 and n = 500. Why?

Questions 3 – 7. Scores for sixth graders on a standardized reading test are normally distributed with m = 75 and s = 10. A teacher suspects that his sixth grade class is reading at an above average level and might need more challenging material. This class of n = 16 students is given the standardized reading test, and the mean for the class is 80 with a standard deviation of 5. On the basis of their standardized test scores, does this class appear to be reading at an above average level?

(3) State the statistical hypotheses (use symbols).

(4) Find the critical value(s) of the test statistic using alpha = .05.

(5) Compute the test statistic.

(6) Make a decision.

(7) Provide a conclusion statement that answers the research question (be sure to include the statistical information necessary to support your conclusion).

Questions 8 – 14. A psychologist hypothesizes that reduced levels of serotonin play a role in aggression. To test this hypothesis, the researcher randomly assigns rats to either a control group or an experimental group. Rats in the control group are given a placebo whereas rats in the experimental group are given a drug that lowers the level of serotonin in the brain. The researcher then records the number of aggressive behaviors displayed by the rats. The sample of n = 8 rats in the control group exhibited an average of 14 aggressive behaviors with SS = 180. The sample of n = 6 rats in the experimental group displayed an average of 22 aggressive behaviors with SS = 108. Does a reduction in serotonin increase aggressive behavior?

(8) State the statistical hypotheses (use symbols).

(9) Find the critical value(s) of the test statistic using alpha = .05.

(10) Compute the test statistic.

(11) Make a decision.

(12) Provide a conclusion statement that answers the research question (be sure to include the statistical information necessary to support your conclusion).

(13) Using a point estimate, how different are the control and experimental groups in terms of their aggressive behaviors?

(14) Construct a 95% confidence interval for these data. What does this indicate about the difference between the groups?

15. A candidate running for mayor claims that she will reduce the average rate of response to emergency calls to less than 30 minutes, which is the average response time (m) under previous mayors. Thanks to this campaign promise, she wins the election. At the end of her first year, it is discovered that a random sample of n = 25 emergencies had a mean response time of 24.5 minutes with a standard deviation of 10 minutes. Did the mayor keep her promise and reliably reduce emergency response? Compute the test statistic that should be used to answer this question.

16. A researcher studies the effect of cognitive psychotherapy on positive self-regard. The number of positive statements made about oneself is recorded for each participant during the initial consult and again after 8 weeks of therapy. The data are below. Does cognitive psychotherapy impact positive self-regard? Compute the test statistic that should be used to answer this question.

# of positive self-statements before therapy # of positive self-statements after therapy

4 5

3 8

6 10

2 4

Questions 17-20. A researcher investigated whether people will naturally follow a 24-hour cycle of sleeping and waking in the absence of normal sunlight patterns and time cues. Participants were asked to live, for two weeks, in an apartment with no natural light and no clocks (or other indications of time). Participants were free to have the interior lights on or off whenever they wished, sleep when they wished, and so on. After two weeks, the length of the sleep-wake cycle was recorded for each participant. An analysis of this data in SPSS yielded the following output.

	Mean	Std Deviation	Std. Error Mean
Sleep-Wake Cycle	26.375	1.5634	0.3496

Test value = 24
t	df	Sig. (2-tailed)	Mean Difference
??	19	0.001	2.375

17. How many participants took part in this study?

18. What is the value of the t-statistic?

19. Should the researcher reject the null or fail to reject on the basis of this analysis?

20. Write a conclusion statement that answers the research question (be sure to include the statistical information necessary to support your conclusion).