Chapter 15, page 328-329, problems 1 & 3

1. A market researcher wants to see whether people in four regions of a city buy the same brand of dish detergent. He takes a random sample of people in the different areas and asks then which of 10 brands (coded from 1 to 10) they purchase most often. He enters the data into SPSS and runs the One-Way ANOVA procedure. The observed significance level for his F value is 0.00001. What can he conclude based on these results?

3. Based on the following table, which groups are significantly different from each other using the Bonferroni test and a significance level of 0.05?

Dependent Variable: STRENGTH

Bonferroni

• The mean difference is significant at the .05 level.

Chapter 15, page 330, problem 1d,g,h, 2, 3, 5, 6a-d

Use the gss.sav data file to answer these questions.  Assume the variances are equal and the distribution is normal.

1. In the General Social Survey people classified themselves as being very happy, pretty happy, or not

(a) Compute basic descriptive statistics for each of the three happiness groups

(b) Make boxplots of age for the three groups

(c) Does the assumption of equal variances in the groups appear reasonable? The assumption of normality?

(d) Perform a one-wav analysis of variance on these data what can you conclude?

Which groups are significantly different from another using the Bonferroni?

(e) From the analysis-of-variance table, estimate the variance of the ages within each happiness group. What is your estimate of the standard deviation within the groups? How does this compare to the actual standard deviations of each group in the table of descriptive statistics?

(f) What are the three sample means that you have observed in the table of descriptive statistics? Based on the three sample means, what is your estimate of the variance of the ages within each happiness group?

(g) What is the value of the ratio of the two variances?

(h) If the null hypothesis is true, how often would you expect to see a ration of sample variances at least this large?

2. Run a one-way analysis of variance to test the null hypothesis that the average years of education (variable educ ) is the same for men and women. Run an independent-samples t test to test the same hypothesis. Compare the results. (If you square the equal-variance t value, you’ll get the F value from the analysis of variance.)

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3. You’re interested in seeing whether there is a relationship between happiness and number of hours of television viewed a day (variables happy and tvhours ). Perform appropriate analyses and summarize your results. Include appropriate descriptive statistics.

6. Consider respondents’ average income (variable rincdol ).

a. Use the Means procedure to calculate average income for different educational levels (variable degree ). What is the average income for all respondents? For people with less than high school degree? For people with a graduate degree?

b. Test null hypothesis that the average income is the same for all degree groups. What assumptions do you have to make?

c. Using the Bonferroni multiple comparison procedure, determine which groups are significantly different from one another. Summarize your findings.

d. Does staying in school pay off?

Chapter 15, page 331, problem 8c & 8d

Use the lib1500.sav data file to answer these questions. You will not be able to open the library.sav data file :

8. Consider the relationship between average age and the categories of library use (variable libusefq).

c. Assume that the necessary assumptions for analysis of variance are met. Can you reject the null hypothesis that, in the population, the average age for people in all library use categories is the same?

d. Use the Bonferroni multiple comparison procedure to determine which groups are significantly different from one another.

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