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Chapter 10: Q. 10.109 (page 440)
State the two conditions required for performing a paired r-procedure. How important are those conditions?
A simple random paired sample with normal differences or a large sample size are required conditions for performing a paired t-procedure. A simple random sample assumption is required.
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Define the phrase independent samples.
Cooling Down. Cooling down with a cold drink before exercise in the heat is believed to help an athlete perform. Researcher 1. Dugas explored the difference between cooling down with an ice slurry (slushy) and with cold water in the article "lce Slurry Ingestion Increases Running Time in the Heat" (Clinical Journal of Sports Medicine, Vol. 21, No, 6, pp. 541-542). Ten male participants drank a flavored ice slurry and ran on a treadmill in a controlled hot and humid environment. Days later, the same participants drank cold water and ran on a treadmill in the same bot and humid environment. The following table shows the times, in minutes, it took to fatigue on the treadmill for both the ice slurry and the cold water.
At the significance level, do the data provide sufficient evidence to conclude that, on average, cold water is less effective than ice slurry For optimizing athletic performance in the heat? (Note; The mean and standard deviation of the paired differences are minutes and minutes, respectively.)
Wing Length. Refer to Exercise 10.86 and find a 99 con fidence interval for the difference between the mean wing lengths c the two subspecies.
In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled f-test, we stated that the variable
cannot be used as a basis for the required test statistic because is unknown. Why can't that variable be used as a basis for the required test statistic?
A variable of two populations has a mean of and a standard deviation of for one of the populations and a mean of and a standard deviation of for the other population. Moreover. the variable is normally distributed in each of the two populations.
a. For independent samples of sizes and , respectively, determine the mean and standard deviation of .
b. Can you conclude that the variable is normally distributed? Explain your answer.
c. Determine the percentage of all pairs of independent samples of sizes and , respectively, from the two populations with the property that the difference between the simple means is between and .
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