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Chapter 11: Q. 47 (page 728)

North Carolina State University studied student performance in a course required by its chemical engineering major. One question of interest was the relationship between time spent in extracurricular activities and whether a student earned a C or better in the course. Here are the data for the 119 students who answered a question about extracurricular activities:

(a) Calculate percentages and draw a bar graph that describes the nature of the relationship between time spent on extracurricular activities and performance in the course. Give a brief summary in words.

b) Explain why you should not perform a chi-square test in this setting.

Short Answer

Expert verified

(a) The most proportion of passing grades is obtained if the activities are between 2and 12hours per week. The least proportion of passing grades is obtained if the activities are more than 12hours per week.

The bar graph is

(b) Expected values not all at least5.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

The proportions in each group are the number of subjects divided by the column total

Create a histogram

The width of each bar is equal and the height is equal to the proportion.

The most proportion of passing grades are obtained if the activities are between 2and 12hours per week. The least proportion of passing grades are obtained if the activities are more than 12hours per week.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

The chi-square test requires that the expected values are at least 5 .

We note that the column total for >12is 8and thus at least one of the expected counts for >12is less than 5.

Thus the chi-square test cannot be applied.

Expected values not all at least 5 .

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Most popular questions from this chapter

The Pennsylvania State University has its main campus in the town of State College and more than 20smaller 鈥渃ommonwealth campuses鈥� around the state. The Penn State Division of Student Affairs polled separate random samples of undergraduates from the main campus and commonwealth campuses about their use of online social networking. Facebook was the most popular site, with more than 80%of students having an account. Here is a comparison of Facebook use by undergraduates at the main campus and commonwealth campuses who have a Facebook account:

Calculate the conditional distribution (in proportions) of Facebook use for each campus setting?

Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed to examine the factors that determine social status for children in grades 4,5, and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions they asked was 鈥淲hat would you most like to do at school: make good grades, be good at sports, or be popular?鈥� The two-way table below summarizes the students鈥� responses.

GoalGenderGradesPopularSportsFemale1309130Male1175060

(a) Construct an appropriate graph to compare male and female responses. Write a few sentences describing the relationship between gender and goals.

(b) Is there convincing evidence of an association between gender and goals for elementary school students? Carry out a test at the localid="1653534557186" 伪=0.05level and report your conclusion.

(c) Which cell contributes most to the chi-square statistic in part (b)? Explain

The P-value for a chi-square goodness-of-fit test is 0.0129. The correct conclusion is

(a) reject H0at 伪=0.05; there is strong evidence that the trees are randomly distributed.

(b) reject H0at 伪=0.05; there is not strong evidence that the trees are randomly distributed.

(c) reject H0at 伪=0.05; there is strong evidence that the trees are not randomly distributed.

(d) fail to reject H0at 伪=0.05; there is not strong evidence that the trees are randomly distributed.

(e) fail to reject H0at 伪=0.05; there is strong evidence that the trees are randomly distributed.

Which of the following may we conclude, based on the test results?

(a) There is strong evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.

(b) HCC either cause cancer directly or is a major contributing factor to the development of cancer in children.

(c) Leukemia is the most common type of cancer among children.

(d) There is not much evidence of an association between wiring configuration and the type of cancer that caused the deaths of children in the study.

Use FacebookMain CampusCommon wealthSeveral times a month or less5576At least once a week215157At least once a day640394Total Facebook users910627

What conclusion would you draw? Justify your answer.
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