10.4 EXERCISES SECTION 10.4 Analysis of Variance 565 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. State the null and alternative hypotheses for a one-way ANOVA test. 2. What conditions are necessary in order to use a one-way ANOVA test? 3. Describe the difference between the variance between samples MSB and the variance within samples MSW. 4. Describe the hypotheses for a two-way ANOVA test. Using and Interpreting Concepts Performing a One-Way ANOVA Test In Exercises 5–14, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. 5. Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes sold in the categories of whitening, cavity prevention, and breath freshening. At a = 0.05, can you conclude that at least one mean cost per ounce is different from the others? (Source: Amazon) Whitening 0.68 1.99 1.38 0.28 5.00 1.23 Cavity prevention 0.70 0.85 0.49 1.43 0.68 Breath freshening 0.66 0.68 1.23 0.45 6. Dog Lifespan The table shows the lengths (in years) of the lives of dogs for a sample of three different breeds. At a = 0.05, is there enough evidence to conclude that at least one of the dog breeds has a mean lifespan that is different from the others? (Adapted from American Kennel Club) Boxer 11.6 10.8 12.9 12.3 16.1 9.9 Bulldog 10.5 13.6 12.3 11.1 11.0 10.7 Rottweiler 9.1 11.0 11.5 10.4 12.2 12.4 7. Vacuum Cleaners The table shows the weights (in pounds) for a sample of vacuum cleaners. The weights are classified according to vacuum cleaner type. At a = 0.01, can you conclude that at least one mean vacuum cleaner weight is different from the others? (Source: Consumer Reports) Bagged upright 21 22 23 21 17 19 Bagless upright 16 18 19 18 17 20 Bagged canister 26 24 23 25 27 21
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