Chapter 11: Q.1.2 (page 698)
Why is it important to compare proportions rather than counts in Question ?
Short Answer
Proportions have been computed to make the comparison and reach at the conclusion.
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Chapter 11: Q.1.2 (page 698)
Why is it important to compare proportions rather than counts in Question ?
Proportions have been computed to make the comparison and reach at the conclusion.
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The -value for a chi-square goodness-of-fit test is . The correct conclusion is
(a) reject at ; there is strong evidence that the trees are randomly distributed.
(b) reject at ; there is not strong evidence that the trees are randomly distributed.
(c) reject at ; there is strong evidence that the trees are not randomly distributed.
(d) fail to reject at ; there is not strong evidence that the trees are randomly distributed.
(e) fail to reject at ; there is strong evidence that the trees are randomly distributed.
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 , and . Researchers administered a questionnaire to a random sample of students 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.
(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" level and report your conclusion.
(c) Which cell contributes most to the chi-square statistic in part (b)? Explain
Many popular businesses are franchises鈥攖hink of McDonald鈥檚. The owner of local franchise benefits from brand recognition, national advertising, and detailed guidelines provided by the franchise chain. In return, he or she pays fees to the franchise firm and agrees to follow its policies. The relationship between the local owner and the franchise firm is spelled out in a detailed contract.
One clause that the contract may or may not contain is the entrepreneur鈥檚 right to an exclusive territory. This means that the new outlet will be the only representative of the franchise in a specified territory and will not have to compete with other outlets of the same chain. How does the presence of an exclusive-territory clause in the contract relate to the survival of the business?
A study designed to address this question collected data from a random sample of new franchise firms. Two categorical variables were measured for each franchisor. First, the franchisor was classified as successful or not based on whether or not it was still offering franchises as of a certain date. Second, the contract each franchisor offered to franchisees was classified according to whether or not there was an exclusive-territory clause. Here are the count data, arranged in a two-way table:
role="math" localid="1650453920307"
Do these data provide convincing evidence of an association between an exclusive territory clause and business survival? Carry out an appropriate test at the level.
Make a bar graph that compares the two conditional distributions. What are the most important differences in Facebook use between the two campus settings?
Representative sample? For a class project, a group of statistics students is required to take an SRS of students from their large high school to take part in a survey. The students鈥 sample consists of freshmen, sophomores, juniors, and seniors. The school roster shows that of the students enrolled at the school are freshmen, are sophomores, are juniors, and are seniors.
(a) Construct a well-labeled bar graph that shows the distribution of grade levels (in percents) for the sample data. Do these data give you any reason to suspect that the statistics students鈥 sample is unusual? Explain. (b) Use an appropriate test to determine whether the sample data differ significantly from the actual distribution of students by grade level at the school.
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