Solved: Performing a One-Way ANOVA Test In Exercises 514, (a) identify the claim and

. State the null and alternative hypotheses for a one-way ANOVA test.

What conditions are necessary in order to use a one-way ANOVA test?

Describe the difference between the variance between samples MSB and the variance within samples MSW.

Describe the hypotheses for a two-way ANOVA test.

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At a = 0.05, can you conclude that at least one mean cost per ounce is different from the others? (Source: Consumer Reports) Very good 0.47 0.49 0.41 0.37 0.48 0.51 Good 0.60 0.64 0.58 0.75 0.46 Fair 0.34 0.46 0.44 0.60

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Automobile Batteries The table shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At a = 0.05, is there enough evidence to conclude that at least one mean battery price is different from the others? (Source: Consumer Reports) Group size 35 90 90 75 105 65 Group size 65 100 75 105 110 90 90 Group size 24/24F 115 75 75 90 110 90

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.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 21 20 Top canister 26 24 23 25 27 21

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Government Salaries The table shows the salaries (in thousands of dollars) for a sample of individuals from the federal, state, and local levels of government. At a = 0.01, can you conclude that at least one mean salary is different from the others? (Adapted from Bureau of Labor Statistics) Federal State Local 70.4 52.9 48.8 63.1 37.0 38.3 74.5 54.0 42.6 82.3 54.5 41.0 81.6 56.7 51.6 85.7 61.8 45.7 56.3 39.9 60.3 71.2 50.4 40.8 80.9 53.6 37.2 64.6 47.4 33.4

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Ages of Professional Athletes The table shows the ages (in years) for a sample of professional athletes from several sports. At a = 0.05, can you conclude that at least one mean age is different from the others? (Source: ESPN) MLB NBA NFL NHL 30 28 26 29 25 27 28 23 26 29 27 26 31 30 26 30 27 24 29 27 29 27 27 25 27 28 26 24 25 33 26 26 27 26 27 29 23 28 27 32 26 27 29 28 34 28 25 25 29 26 24 27

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology. Cost Per Mile The table shows the costs per mile (in cents) for a sample of automobiles. At a = 0.01, can you conclude that at least one mean cost per mile is different from the others? (Adapted from American Automobile Association) Small sedan Medium sedan Large sedan SUV 4WD Minivan 43 67 64 87 66 41 49 73 66 76 49 63 83 75 59 54 59 75 78 51 46 64 80 70 52 72

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Well-Being Index The well-being index is a way to measure how people are faring physically, emotionally, socially, and professionally, as well as to rate the overall quality of their lives and their outlooks for the future. The table shows the well-being index scores for a sample of states from four regions of the United States. At a = 0.10, can you reject the claim that the mean score is the same for all regions? (Adapted from Gallup and Healthways)

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Days Spent at the Hospital In a recent study, a health insurance company investigated the number of days patients spent at the hospital. In part of the study, the company selected a sample of patients from four regions of the United States and recorded the number of days each patient spent at the hospital. The table shows the results of the study. At a = 0.01, can the company reject the claim that the mean number of days patients spend at the hospital is the same for all four regions? (Adapted from National Center for Health Statistics) Northeast Midwest South West 6 6 3 3 4 6 5 4 7 7 6 6 2 3 6 4 3 5 3 6 4 4 7 6 6 4 4 5 8 3 2 9 2 Northeast Midwest South West 67.6 66.6 64.2 66.1 67.3 67.6 64.1 67.4 68.4 65.6 65.8 69.7 66.2 68.9 66.1 68.5 66.5 65.5 62.7 65.2 68.6 68.5 68.0 66.7 67.4 63.6 67.1 68.0 65.2 68.8 65.2 67.7 64.0 66.6

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Personal Income The table shows the salaries of a sample of individuals from six large metropolitan areas. At a = 0.05, can you conclude that the mean salary is different in at least one of the areas? (Adapted from U.S. Bureau of Economic Analysis) Chicago Dallas Miami Denver San Diego Seattle 43,581 36,524 49,357 37,790 48,370 57,678 37,731 33,709 53,207 38,970 45,470 48,043 46,831 40,209 40,557 42,990 43,920 45,943 53,031 51,704 52,357 46,290 54,670 52,543 52,551 40,909 44,907 49,565 41,770 57,418 42,131 53,259 48,757 40,390 47,269 53,557

Performing a One-Way ANOVA Test In Exercises 514, (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. If convenient, use technology.Housing Prices The table shows the sale prices (in thousands of dollars) of a sample of one-family houses in three cities. At a = 0.10, can you conclude that at least one mean sale price is different from the others? (Adapted from National Association of Realtors) Gainesville Orlando Tampa 139.0 169.9 184.7 111.5 127.1 69.7 156.6 111.3 165.0 152.3 113.5 157.5 214.7 133.9 103.9 172.4 160.8 120.8 52.8 179.2 88.1 170.6 70.7 168.2 140.5 89.9 59.5 186.0 99.3 170.2 139.0

Using Technology to Perform a Two-Way ANOVA Test In Exercises 1518, use technology and the block design to perform a two-way ANOVA test. Use a = 0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.Advertising A study was conducted in which a sample of 20 adults was asked to rate the effectiveness of advertisements. Each adult rated a radio or television advertisement that lasted 30 or 60 seconds. The block design shows these ratings (on a scale of 1 to 5, with 5 being extremely effective). 30 sec 2, 3, 5, 1, 3 3, 5, 4, 1, 2 60 sec 1, 4, 2, 2, 5 2, 5, 3, 4, 4

Using Technology to Perform a Two-Way ANOVA Test In Exercises 1518, use technology and the block design to perform a two-way ANOVA test. Use a = 0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.Vehicle Sales The owner of a car dealership wants to determine whether the gender of a salesperson and the type of vehicle sold affect the number of vehicles sold in a month. The block design shows the numbers of vehicles, listed by type, sold in a month by a sample of eight salespeople. Male 6, 5, 4, 5 2, 2, 1, 3 4, 3, 4, 2 Female 5, 7, 8, 7 1, 0, 1, 2 4, 2, 0, 1

Using Technology to Perform a Two-Way ANOVA Test In Exercises 1518, use technology and the block design to perform a two-way ANOVA test. Use a = 0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.Grade Point Average A study was conducted in which a sample of 24 high school students was asked to give their grade point average (GPA). The block design shows the GPAs of male and female students from four different age groups. Male 2.5, 2.1, 3.8 Female 4.0, 2.1, 1.9 15 4.0, 1.4, 2.0 3.5, 3.0, 2.1 16 17 18 3.5, 2.2, 2.0 4.0, 2.2, 1.7 3.1, 0.7, 2.8 Gender 1.6, 2.5, 3.6

Using Technology to Perform a Two-Way ANOVA Test In Exercises 1518, use technology and the block design to perform a two-way ANOVA test. Use a = 0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.Disk Drive Repairs The manager of a computer repair service wants to determine whether there is a difference in the time it takes four technicians to repair different brands of disk drives. The block design shows the times (in minutes) it took for each technician to repair three disk drives of each brand. Brand A 67, 82, 64 42, 56, 39 69, 47, 38 44, 62, 55 47, 58, 62 55, 45, 66 70, 44, 50 Brand B 47, 29, 40 Brand C 47, 36, 68 39, 74, 51 74, 80, 70 45, 62, 59

Use the information above to solve Exercises 19 22.Refer to the data in Exercise 5. At a = 0.05, perform a Scheff Test to determine which means have a significant difference.

Use the information above to solve Exercises 19 22.Refer to the data in Exercise 7. At a = 0.01, perform a Scheff Test to determine which means have a significant difference.

Use the information above to solve Exercises 19 22.Refer to the data in Exercise 8. At a = 0.01, perform a Scheff Test to determine which means have a significant difference.

Use the information above to solve Exercises 19 22.Refer to the data in Exercise 11. At a = 0.10, perform a Scheff Test to determine which means have a significant difference.