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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: 5 4 5 7 5 4 3

Married: 2 1 2 2 3 1 2

Divorced: 6 7 7 8 6 5 4

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.

___ CHOICES ARE:INDEPENDENT, ISOLATED, STRATIFIED, DEPENDENT, ____ CHOICES ARE: EXCLUSIVE, RANDOM, STATISTICAL, COMPLETE samples. Level of measurement is____ CHOICES ARE INETERVAL-RATIO, CATEGORICAL, NUMERIC, ORDINAL.

Populations are___ CHOICES ARE: UNIFORMLY, EXPONENTIALLY, NORMALLY, RANDOMLYdistributed. Population variances are __CHOICES ARE: EQUAL, INDEPENDENT, UNKNOWN, SMALL.

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 notassumethese 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?ibe the mean number of hours spent watching TV or using the Internet. The null hypothesis for your ANOVA would be as follows:

H0:____ CHOICES ARE: SCREENSHOT CAPTURE 2 .

In the context of this study, which translation is correct? CHOOSE THE ONE THAT APPLIES:

The average time spent watching TV or using the Internet differs, depending on marital status.

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.

Single people spend as much time watching TV or using the Internet as married people.

The alternative hypothesis isH1: CHOOSE THE ONE THAT APPLIES:

All three of the population means are the same.

At least one of the population means is different.

All three of the population means are different.

At least one of the sample means is different.

Step 3. Selecting the Sampling Distribution and Establishing the Critical Region

The sampling distribution for ANOVA is the___ CHOICES ARE: P, T, Z, F distribution.

The degrees of freedom within is dfw = __ CHOICES ARE: 7, 21, 18, 2.

The degrees of freedom between is dfb =___ CHOICES ARE: 2, 21, 7, 18.

If you set the significance level alpha to 0.05, then the critical F score is F(critical) =___ CHOICES ARE: 3.55, 6.01, 24.12, 25.924.

Step 4. Computing the Test Statistic

This step involves several computations, which you perform one at a time as follows:

SST =___ CHOICES ARE: 467, 66.675, 89.826, 23.151; SSB =___ CHOICES ARE: 467, 23.151, 66.675, 89.826; SSW = __ CHOICES ARE: 467, 23.151, 89.826, 66.675

The mean square estimates are as follows: Mean square within = ___ CHOICES ARE: 1.286, 23.151, 44.913, 33.338; mean square between = ___ CHOICES ARE: 66.675, 33.338, 44.913, 1.286

The obtained test statistic is F(obtained) =___ CHOICES ARE: 34.925, 0.039, 25.924, 3.55

Step 5. Making a Decision and Interpreting the Results

Compare the test statistic with the critical value (enter the values you calculated previously):

Critical: ___ CHOICES ARE: 24.12, 6.01, 3.55, 25.924

Obtained:___ CHOICES ARE: 25.924, 0.039, 34.925, 3.55

The test statistic falls ___ CHOICES ARE: OUTSIDE, WITHINthe critical region, so your decision should be to ___ CHOICES ARE: FAIL TO REJECT, REJECT, CONFIRM, PROVE the null hypothesis.

In the context of this study, which of the following statements is accurate? PLEASE CHOOSE ONE:

The average time spent watching TV or using the Internet does not differ significantly by marital status.

Single people spend as much time watching TV or using the Internet as married people.

The average time spent watching TV or using the Internet differs significantly by marital status.

The average time spent watching TV or using the Internet is the same, regardless of marital status.

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