You can increase your BMR by implementing one of the following strategies: Strategy 1: Having the appropriate amount of water will increase or boost metabolism and regulate body temperature. Strategy 2: The more frequently you eat, the greater your metabolism will become to burn fat and calories. Aim for 6-8 small meals with protein, veggies, and good fats. Strategy 3: Ingesting complete protein, whole wheat, and spicy foods increases BMR. Strategy 4: Cold and hot hydrotherapy boosts or increases BMR. Strategy 5: Caffeine, nicotine, and some fat-burning supplements will increase metabolism. A registered dietician took a random sample of six females. These strategies were compared using a completely randomized design. The data are shown in the table below. 

The dietician was interested in knowing whether the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions.

a. Do the data provide sufficient evidence to indicate a difference in location for at least two of the five strategies? Test using the Kruskal-Wallis H statistic with a = 0.05.

b. What is the most accurate statement that can be made about the p-value of this test?

c. Explain how to use the p-value for testing the hypotheses.

d. Perform an analysis of variance and give the ANOVA table for the analysis, and using statistical software to approximate the p-value for the F statistic in testing the equality of the means test using a = 0.05.

e. Compare the p-values for the tests in parts

(a) and (d). Another registered dietician also planned to evaluate five different strategies to assess their effectiveness in increasing or boosting BMR. However, this dietician consulted a statistician about the design of her study. Because she was looking for an effective method of increasing BMR, the statistician suggested she should divide the subjects into groups according to their age. These age groups represent relatively homoge- neous experimental units within which the comparison of different ways to increase the BMR may be made. Within each age group, the five participating females were randomly assigned to the five strategies and measurements of BMR were recorded. The data is summarized in the following table.

a. What experimental design did the statistician use?

b. The dietician wasn't sure whether the assumptions for the usual analysis of variance were valid, so she decided to use a nonparametric procedure. Use the appropriate method to determine whether the BMR is the same for all the strategies. Use = 0.05.

c. Can we conclude that all the strategies are equally effective?

d. What is the observed significance level of this test?

e. The dietician would like to perform an analysis of variance anyway. Give the ANOVA table for the analysis, using statistical software to approximate the p-value for the F statistic in testing the equality of the five treatment means. Test using = 0.05.

f. Compare the p-values for the tests in parts

(b) and (e).

Transcribed Image Text:

Strategy 1 Strategy 2 Strategy 3 Strategy 4 Strategy 5 998 1001 877 1129 1009 1055 955 1151 1098 905 975 1099 1173 1012 1191 1123 987 890 981 993 1074 1134 1089 1034 1143 1101 1195 1188 995 1159