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Chapter 12: Q4BSC (page 566)
Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not?
Yes, the given experiment is a balanced design as the number of observations under the given two factors is equal.
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b. compare your results in part (a) for and with those you obtained in Exercises , where you employed the defining formulas.
c. construct a one-way table.
d. decide, at the significance level, whether the data provide sufficient evidence to conclude that the means of the populations from which the samples were drawn are not all the same.
Arsenic in Rice Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different states? Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem?
Arkansas | 4.8 | 4.9 | 5 | 5.4 | 5.4 | 5.4 | 5.6 | 5.6 | 5.6 | 5.9 | 6 | 6.1 |
California | 1.5 | 3.7 | 4 | 4.5 | 4.9 | 5.1 | 5.3 | 5.4 | 5.4 | 5.5 | 5.6 | 5.6 |
Texas | 5.6 | 5.8 | 6.6 | 6.9 | 6.9 | 6.9 | 7.1 | 7.3 | 7.5 | 7.6 | 7.7 | 7.7 |
Cola Weights Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic?
Speed Dating
Listed below are attribute ratings of males by females who participated in speed dating events (from Data Set 18 鈥淪peed Dating鈥� in Appendix B). Use a 0.05 significance level to test the claim that females in the different age brackets give attribute ratings with the same mean. Does age appear to be a factor in the female attribute ratings?
Age 20-22 | 38 | 42 | 30.0 | 39 | 47 | 43 | 33 | 31 | 32 | 28 |
Age 23-26 | 39 | 31 | 36.0 | 35 | 41 | 45 | 36 | 23 | 36 | 20 |
Age 27-29 | 36 | 42 | 35.5 | 27 | 37 | 34 | 22 | 47 | 36 | 32 |
Empty Stomachs. In the publication "How Often Do Fishes 'Run on Empty'?' (Ecology, Vol. , No , Pp. ), D. Arrington et al. examined almost fish of species from the waters of Africa, South and Central America, and North America to determine the percentage of fish with empty stomachs. The fish were classified as piscivores (fish-eating), invertivores (invertibrateeating), omnivores (anything-eating) and algivores/detritivores (eating algae and other organic matter). For those fish in African waters, the data on the WeissStats site give the proportions of each species of fish with empty stomachs. At the significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean percentages of fish with empty stomachs among the four different types of feeders?
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