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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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Refer again to Fig. 10.8 on page 427, where each pair of graphs shows the distributions of a variable on two populations. Suppose that, in each case, you want to perform a small-sample hypothesis test based on independent simple random samples to compare the means of the two populations. In each case, decide which, if any, of the following tests is preferable: the pooled -test, the non pooled -test, or the Mann-Whitney test. Explain your answers.
Recess and Wasted Food, E. 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?
Gasoline Additive. This exercise shows what can happen when a hypothesis-testing procedure designed for use with independent samples is applied to perform a hypothesis test on a paired sample. The gas mileages, in miles per gallon (mpg), of 10 randomly selected cars, both with and without a new gasoline additive, are shown in the following table.
In Exercises 10.25-10.30, hypothesis tests are proposed. For each
hypothesis test,
a. identify the variable.
b. identify the two populations,
c. determine the null and alternative hypotheses.
d. classify the hypothesis test as two-tailed, left-tailed, or right-tailed.
Teaching Duties. Contingent faculty members in higher education are non-tenure track faculty, adjuncts, postdocs, lecturers, of instructors. R. Bowden and L. Gonzalez researched whether contingent faculty members are different from tenure-track faculty members with regards to teaching, research, and service in the article "The Rise of Contingent Faculty: Its Impact on the Professoriate and Higher Education" (Journal of Applied Research in Higher Education, Vol. 4, No. 1, pp. 5-22). A hypothesis test was conducted to decide whether the mean number of classes taught for credit per semester was less for contingent faculty than for tenure-track faculty.
Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in the National Household Travel Survey, Summary of Travel Trends. Independent random samples of midwestern households and southern households provided the following data on last year's VMT, in thousands of miles.
At the significance level, does there appear to be a difference in last year's mean VMT for midwestern and southern households? (Note: , and .)
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