HW 9 Stats

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You must use software to solve these problems. Copy/paste the output to include with your answer. Answers without the results will receive zero credit. On the other hand, copy/pasted output without any interpretation will receive zero credit. Ch 9 homework problems (5 points each) 9.2 Physical education requirements. In addition to what is in the problem statement graph the data in a side-by-side bar plot and carry out the analyses through the chi square test. State Ho and Ha. Carry out the test. Interpret your findings. 9.2 Physical education requirements. In Exercise 8.41 (page 482), you analyzed data from a study that included 354 higher education institutions: 225 private and 129 public. Among the private institutions, 60 required a physical education course, while among the public institutions, 101 required a course. Your analysis in that exercise focused on the comparison of two proportions. Use these data to construct a two-way table for analysis and find the joint distribution, the marginal distributions, and the conditional distributions . Use these distributions to give a brief summary of the relationship between the type of institution and whether a physical education course is required Ho: Physical education requirements are not associated with the type of school Ha: Physical educations requirements are associated with the type of school. Private Public Total Required 60 101 161 Not required 165 28 193 Total 225 129 354 X-squared = 86.068, df = 1, p-value < 2.2e-16 Marginal distribution of school type: 225 private and 129 public Marginal distribution of physical education status: 161 required and 193 not required Conditional distribution: Probability that a private school requires physical ed : 60/225= .266 Probability that a private school does not require physical ed: 165/225= .733 Probability that a public school requires physical ed: 101/129= .783 Probability that a public school does not require physical ed: 28/129= .217 Probability that a school that requires physical ed is public: 101/161= .627 Probability that a school that requires physical ed is private: 60/161= .372 Probability that a school that does not require physical ed is public: 28/193= .145 Probability that a school that does not require physical ed is private: 165/193=.855 Joint distribution: 60 private and require, 101 public and required, 165 private and not required, 28 public and not required The p-value is approximately zero which means we reject the null. Reject Ho; there is evidence that physical education requirements are associated with the type of school.
Summary: Private schools tend to be more associated with not requiring physical education programs while public schools tend to be more associated with requiring physical education 9.26 Is there a random distribution of trees a-c 9.26 Is there a random distribution of trees? In Example 6.1 (page 329), we examined data concerning the longleaf pine trees in the Wade Tract and concluded that the distribution of trees in the tract was not random . Here is another way to examine the same question. First, we divide the tract into four equal parts, or quadrants, in the east–west direction. Call the four parts Q1 through Q4. Then we take a random sample of 100 trees and count the number of trees in each quadrant. Here are the data: Quadrant Q1 Q2 Q3 Q4 Count 18 22 39 21 a. If the trees are randomly distributed, we expect to find 25 trees in each quadrant. Why? Explain your answer. a. The trees are randomly distributed meaning it is equally likely for a tree to be in each quadrant. This means out of 100 trees, we must have approximately equal number of tress per quadrant equally splitting it up to 25 per quadrant. b. We do not really expect to get exactly 25 trees in each quadrant. Why? Explain your answer.
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