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Chapter 10: Q.10.71 (page 427)
The sample standard deviations are and .
A non-pooled test should be utilised.
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Bergman et al. conducted a study to determine, among other things, the impact that scheduling recess before or after the lunch period has on wasted food for students in grades three through five. Results were published in the online article "The Relationship of Meal and Recess Schedules to Plate Waste in Elementary Schools" (Journal of Child Nutrition and Management, Vol. 28, Issue 2). Summary statistics for the amount of food wasted, in grams, by randomly selected students are presented in the following table.
At the significance level, do the data provide sufficient evidence to conclude that, in grades three through five, the mean amount of food wasted for lunches before recess exceeds that for lunches after recess?
In the paper "The Relation of Sex and Sense of Direction to Spatial Orientation in an Unfamiliar Environment" (Journal of Environmental Psychology, Vol. 20, pp. 17-28), J. Sholl et al. published the results of examining the sense of direction of 30 male and 30 female students. After being taken to an unfamiliar wooded park, the students were given some spatial orientation tests, including pointing to the south, which tested their absolute frame of reference. The students pointed by moving a pointer attached to a protractor. Following are the absolute pointing errors, in degrees, of the participants.
At the significance level, do the data provide sufficient evidence to conclude that, on average, males have a better sense of direction and, in particular, a better frame of reference than females? (Note: .)
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.
Left-Tailed Hypothesis Tests and CIs. If the assumptions for a pooled -interval are satisfied, the formula for a -level upper confidence bound for the difference, , between two population means is
For a left-tailed hypothesis test at the significance level , the null hypothesis will be rejected in favor of the alternative hypothesis if and only if the -level upper confidence bound for is less than or equal to . In each case, illustrate the preceding relationship by obtaining the appropriate upper confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.
a. Exercise 10.45
b. Exercise 10.46
O. Ehimwenma and M. Tagbo, researchers in Nigeria, were interested in how the characteristics of the spleen of residents in their tropical environment compare to those found elsewhere in the world. They published their findings in the article "Determination of Normal Dimensions of the Spleen by Ultrasound in an Endemic Tropical Environment" (Nigerian Medical Journal, Vol. 52, No. 3, pp. 198-203). The researchers randomly sampled males and females in Nigeria. The mean and standard deviation of the spleen lengths for the males were and respectively, and those for the females were and , respectively. At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean spleen lengths of male and female Nigerians?
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