statictis

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1. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 36 preferred the Half Pint lager, 35 preferred the XXX lager, and 9 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) $\chi_{obt}^2$ = State the decision to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

2. A psychologist studying addiction tests whether cravings for cocaine and relapse are independent. The following table lists the observed frequencies in the small sample of people who use drugs.

Obs. Freq.	Relapse
	Yes	No
Cravings	Yes	20	13	33
	No	8	17	25
	28	30	N = 58

(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) $\chi_{obt}^2$ = Decide whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

(b) Compute effect size using ϕ and Cramer's V. Hint: Both should give the same estimate of effect size. (If necessary, round your intermediate steps to two or more decimal places. Round your answers to two decimal places.)

ϕ	=
V	=

3. A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test.

	Noise Level
	Low	Medium	High
Exam	Pass	20	18	8	46
	Fail	8	6	10	24
	28	24	18	N = 70

(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) $\chi_{obt}^2$ = Decide whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

(b) Compute effect size using Cramer's V. (Round your answer to two decimal places.) V =

4. What is Cramer's V for each of the following values for the chi-square test for independence? (Round your answers to two decimal places.)

(a)

X2 = 7.49, n = 110, dfsmaller = 2

V = (b)

X2 = 5.87, n = 80, dfsmaller = 1

V = (c)

X2 = 12.61, n = 160, dfsmaller = 3

V =

5. Altamura, Dell'Osso, Vismara, and Mundo (2008) measured the relationship between gender and duration of untreated illness among a sample of those suffering from major depressive disorder. The following table lists the observed frequencies from this study.

	Duration of Untreated Illness
	≤ 12 Months	> 12 Months
Gender	Men	20	5	25
	Women	55	33	88
	75	38	N = 113

Compute a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) $\chi_{obt}^2$ = Decide whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

6. Which nonparametric tests can be computed using a normal approximation formula to compute the test statistic? (Select all that apply.)

sign testWilcoxon signed-ranks T testKruskal-Wallis H testMann-Whitney U testFriedman test

7. A community psychologist selects a sample of 16 local police officers to test whether their physical endurance is better than the median score of 72. She measures their physical endurance on a 100-point physical endurance rating scale.

Performance Scores
53	54	89	70
61	84	85	80
87	86	81	92
83	76	91	93

Based on the data given above, compute the one-sample sign test at a 0.05 level of significance. x = State whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

8. Practitioners measured spiritual well-being (SWB) in a sample of 16 adults who were alcoholic before and following treatment for alcoholism.

Change in SWB Following Treatment
+9	+11
−8	−3
−5	+7
+20	+14
−6	+12
+15	+13
−1	−4
−2	+10

Use the normal approximation for the Wilcoxon signed-ranks T test to analyze the data above. (Round your answer to two decimal places.) z = State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis.Reject the null hypothesis.

9. A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

With Microsoft PowerPoint	Without Microsoft PowerPoint
7	14
21	23
5	10
9	18
8	12
13	11
19	6
4	15

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.) z = State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

Retain the null hypothesis.Reject the null hypothesis.

10. A statistics instructor measured student attitudes toward a statistics course prior to lectures, at the midterm, and after the final exam. Attitudes were measured on a 16-point scale, with higher scores indicating more positive attitudes toward the statistics course.

Student	Prior to Lectures	At the Midterm	After the Final
A	6	5	10
B	4	10	14
C	8	12	13
D	12	11	15
E	5	7	10

Based on the results shown in the table, test whether or not attitudes differed using the Friedman test at a 0.05 level of significance. (Round your answer to two decimal places.) $\chi_{R}^2$ = State whether to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.

11. An instructor tests whether class attendance (low, average, high) and grade point average (low, average, high) are independent.

State the degrees of freedom for the test. df =