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Chapter 13: Problem 1

Descriptions of four studies are given. In each of the studies, the two populations of interest are the students at a particular university who live on campus and the students who live off campus. Which of these studies have samples that are independently selected? Study 1: To determine if there is evidence that the mean amount of money spent on food each month differs for the two populations, a random sample of 45 students who live on campus and a random sample of 50 students who live off campus are selected. Study 2: To determine if the mean number of hours spent studying differs for the two populations, a random sample students who live on campus is selected. Each student in this sample is asked how many hours he or she spend working each week. For each of these students who live on campus, a student who lives off campus and who works the same number of hours per week is identified and included in the sample of students who live off campus. Study 3: To determine if the mean number of hours worked per week differs for the two populations, a random sample of students who live on campus and who have a brother or sister who also attends the university but who lives off campus is selected. The sibling who lives on campus is included in the on campus sample, and the sibling who lives off campus is included in the off- campus sample. Study 4: To determine if the mean amount spent on textbooks differs for the two populations, a random sample of students who live on campus is selected. A separate random sample of the same size is selected from the population of students who live off campus.

Short Answer

Expert verified
Study 1 and Study 4 use independently selected samples. Study 2 and Study 3 do not.

Step by step solution

01

Analysis of Study 1

In Study 1, two random samples of students are taken, one from the 'on-campus' group and one from the 'off-campus' group. There is no mention of any relation or factor that connects the students selected in the two groups, marking them as independently selected samples.
02

Analysis of Study 2

Study 2 involves selecting students from the 'on-campus' group randomly, and then each 'off-campus' student is specifically picked based on the hours worked by the 'on-campus' students. Therefore, the selection of 'off-campus' students is dependent on the 'on-campus' students, making these dependent samples.
03

Analysis of Study 3

In Study 3, a student is chosen from 'on-campus', and then their sibling from 'off-campus' is selected. Here, the selection in one group directly determines the selection in the other group. This marks these as dependent samples.
04

Analysis of Study 4

In Study 4, separate random samples are taken from 'on-campus' and 'off-campus' groups, and there is no relation between the students of the two groups. Therefore, these are independently selected samples.

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Most popular questions from this chapter

The paper "Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children in a National Household Survey" (Pediatrics [2004]: \(112-118\) ) investigated the effect of fast-food consumption on other dietary variables. For a representative sample of 663 teens who reported that they did not eat fast food during a typical day, the mean daily calorie intake was 2,258 and the sample standard deviation was \(1,519 .\) For a representative sample of 413 teens who reported that they did eat fast food on a typical day, the mean calorie intake was 2,637 and the standard deviation was \(1,138 .\) Use the given information and a \(95 \%\) confidence interval to estimate the difference in mean daily calorie intake for teens who do eat fast food on a typical day and those who do not.

In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work (University of Central Florida Undergraduate Research Journal, Spring 2005): $$ \begin{array}{cccc} & \begin{array}{c} \text { Sample } \\ \text { Size } \end{array} & \begin{array}{c} \text { Mean } \\ \text { GPA } \end{array} & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} \\ \begin{array}{c} \text { Students Who Are } \\ \text { Employed } \end{array} & 184 & 3.12 & 0.485 \\ \begin{array}{c} \text { Students Who Are } \\ \text { Not Employed } \end{array} & 114 & 3.23 & 0.524 \\ & & & \end{array} $$ The samples were selected at random from working and nonworking students at the University of Central Florida. Estimate the difference in mean GPA for students at this university who are employed and students who are not employed.

The authors of the paper "Ultrasound Techniques Applied to Body Fat Measurement in Male and Female Athletes" (Journal of Athletic Training [2009]: \(142-147\) ) compared two different methods for measuring body fat percentage. One method uses ultrasound and the other method uses X-ray technology. The accompanying table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Do these data provide convincing evidence that the mean body fat percentage measurement differs for the two methods? Test the appropriate hypotheses using \(\alpha=0.05\). $$ \begin{array}{crr} \text { Athlete } & \text { X-ray } & \text { Ultrasound } \\ \hline 1 & 5.00 & 4.75 \\ 2 & 7.00 & 3.75 \\ 3 & 9.25 & 9.00 \\ 4 & 12.00 & 11.75 \\ 5 & 17.25 & 17.00 \\ 6 & 29.50 & 27.50 \\ 7 & 5.50 & 6.50 \\ 8 & 6.00 & 6.75 \\ 9 & 8.00 & 8.75 \\ 10 & 8.50 & 9.50 \\ 11 & 9.25 & 9.50 \\ 12 & 11.00 & 12.00 \\ 13 & 12.00 & 12.25 \\ 14 & 14.00 & 15.50 \\ 15 & 17.00 & 18.00 \\ 16 & 18.00 & 18.25 \end{array} $$

Babies born extremely prematurely run the risk of various neurological problems and tend to have lower IQ and verbal ability scores than babies that are not premature. The article "Premature Babies May Recover Intelligence, Study Says" (San Luis Obispo Tribune, February 12,2003 ) summarized medical research that suggests that the deficits observed at an early age may decrease as children age. Children who were born prematurely were given a test of verbal ability at age 3 and again at age 8 . The test is scaled so that a score of 100 would be average for normal-birth-weight children. Data for 50 children who were born prematurely were used to generate the accompanying Minitab output, where Age 3 represents the verbal ability score at age 3 and Age8 represents the verbal ability score at age \(8 .\) Use the Minitab output to determine if there is convincing evidence that the mean verbal ability score for children born prematurely increases between age 3 and age 8 . You can assume that it is reasonable to regard the sample of 50 children as a random sample from the population of all children born prematurely. $$ \begin{aligned} &\text { Paired T-Test and Cl: Age8, Age3 }\\\ &\begin{array}{l} \text { Paired } T \text { for } \text { Age8 - Age3 } \\ \begin{array}{rrrrr} & \text { N } & \text { Mean } & \text { StDev } & \text { Se Mean } \\ \text { Age8 } & 50 & 97.21 & 16.97 & 2.40 \\ \text { Age3 } & 50 & 87.30 & 13.84 & 1.96 \\ \text { Difference } & 50 & 9.91 & 22.11 & 3.13 \\ \text { T-Test of mean difference } & =0(\mathrm{vs}>0): \text { T-Value }=3.17 \\ \text { P-Value }=0.001 & & & \end{array} \end{array} \end{aligned} $$

The paper referenced in the previous exercise also gave information on calorie content. For the sample of Burger King meal purchases, the mean number of calories was 1,008 , and the standard deviation was \(483 .\) For the sample of McDonald's meal purchases, the mean number of calories was 908 , and the standard deviation was 624 . Based on these samples, is there convincing evidence that the mean number of calories in McDonald's meal purchases is less than the mean number of calories in Burger King meal purchases? Use \(\alpha=0.01\).
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