Exam 16: Analysis of Variance Anova

Determine the specified calculation. -

Compute the sum of squares. -A one-way ANOVA is to be performed. Independent random samples are selected from four different populations. The sample data are given in the table below. Sample 1 Sample 2 Sample 3 Sample 4 2 4 3 3 5 5 5 9 8 1 4 8 6 7 Compute the treatment sum of squares, SSTR.

A one-way ANOVA is to be performed. Independent random samples are taken from two populations. The sample data are depicted in the dotplot below. Is it reasonable to conclude that the difference between the sample means is due to a difference between the population means and not to variation within the populations? Do you think the null hypothesis would be rejected? Explain your thinking. Sample from population 1 (mean = 12.75) Sample from population 2 $(\text { mean }=19.25)$

Determine the specified calculation. -

Perform a Kruskal-Wallis test using the critical-value approach. -The table below shows the weights (in pounds)of 6 randomly selected women in each of three different age groups. At the 0.01 significance level, do the data provide sufficient evidence to conclude that a difference exists between the three population means? 18-34 35-55 56 and older 119 123 140 134 147 128 114 135 159 125 110 134 153 154 120 138 163 116

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different. -Perform a Tukey multiple comparison to compare the lifetimes of flashlight batteries of three different brands. Use a family confidence level of 0.95. Independent random samples of batteries of the three different brands yielded the following lifetimes in hours. Brand A Brand B Brand C 38 32 24 36 27 25 31 28 29 42 26 29

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied. UseMinitab to perform the required hypothesis test using the p-value approach. -Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below. Test the claim that the four different models have the same population mean. Use a significance level of 0.05.

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach. -The data below represent the weight losses for people on three different exercise programs. At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach. -At the 0.025 significance level, do the data provide sufficient evidence to conclude that a difference exists between the population means of the three different brands? The sample data are given below.

Preliminary data analyses indicate that it is reasonable to consider the assumptions for one-way ANOVA satisfied.Perform the required hypothesis test using the critical-value approach. -Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Test the claim that the type of fertilizer makes no difference in the mean number of raspberries per plant. $\text { Use } \alpha = 0.01$ Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 6 8 6 3 7 5 3 5 6 5 2 3 5 5 3 4 7 5 4 4 6 6 3 5

Conduct a Tukey multiple comparison. Display the confidence intervals in a table. State which population means can bedeclared different. -Perform a Tukey multiple comparison to compare the SAT math scores of students at three different schools. Use a 99% family confidence level. Independent random samples of students from the three different schools yielded the following SAT math scores. School A School B School C 420 600 454 390 540 385 365 665 400 462 510 490 480 515 466