3. Five steps of ANOVA Suppose you are interested in how a person's marital status is related to his or her leisure activities. You randomly sample 21 adults and determine the number of hours each person spends per day watching TV or using the Internet for nonwork activities. The data are shown in the following table: Single Married Divorced 4 5 4 5 7 2 7 1 3 6 6 5 3 8 2 4 9 1 2 6 3 Conduct an ANOVA test for these data using the five-step computational process. Step 1. Making Assumptions and Meeting Test Requirements Complete the following statements about the general assumptions required for ANOVA. Independent W random W samples Level of measurement is interval-ratio v Populations are __normally W distributed Population variances are equal v As the designer of this research project, it is your responsibility to ensure that each of these conditions is met before you perform your analysis. You should not assume these conditions are met; rather, you should verify them as part of your research. Step 2. Stating the Null Hypothesis For each population category (single, married, or divorced), let |; be the mean number of hours spent watching TV or using the Internet. The null hypothesis for your ANOVA would be as follows: Hp: W= =3 v . In the context of this study, which translation is correct? O single people spend as much time watching TV or using the Internet as married people. O single people spend the least time watching TV or using the Internet. @ The average time spent watching TV or using the Internet is the same, regardless of marital status. (O The average time spent watching TV or using the Internet differs, depending on marital status. The alternative hypothesis is H; : O All three of the population means are different. (O All three of the population means are the same. (O At least one of the sample means is different. @ At least one of the population means is different. Step 3. Selecting the Sampling Distribution and Establishing the Critical Region The sampling distribution for ANOVA is the F distribution. The degrees of freedom within is dfw = 18 + The degrees of freedom between is dfb = 2 If you set the significance level alpha to 0.05, then the critical F score is F(critical) = 3.55 W Step 4. Computing the Test Statistic This step involves several computations, which you perform one at a time as follows: SST= 68.490 ;SSB= 34.573 ;SS5W-= v The mean square estimates are as follows: Mean square within = , mean square between = The obtained test statistic is F(obtained) = v Step 5. Making a Decision and Interpreting the Results Compare the test statistic with the critical value (enter the values you calculated previously): Critical: w Obtained: v The test statistic falls W the critical region, so your decision should be to w the null hypothesis. In the context of this study, which of the following statements is accurate? (O The average time spent watching TV or using the Internet differs significantly by marital status. (O single people spend as much time watching TV or using the Internet as married people. (O The average time spent watching TV or using the Internet is the same, regardless of marital status. O The average time spent watching TV or using the Internet does not differ significantly by marital status