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# Testing Goodness-of-Fit with a Normal Distribution Refer ## Problem 25BSC Chapter 11.2

Elementary Statistics | 12th Edition

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Problem 25BSC

Testing Goodness-of-Fit with a Normal Distribution? Refer to Data Set 1 in Appendix B for the 40 heights of females. G r L 1 1 e e 5 6 a s 5 2 H t s . . e e T 4 0 i r h 1 0 g T a 0 5 h h n - - t a 1 1 1 ( n 5 6 6 c 1 5 2 8 m . . . 6 ) 8 4 0 6 . 1 0 0 6 0 5 1 0 1 F r e q u e n c y a. Enter the observed frequencies in the preceding table. b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class. c. Using the probabilities found in part (b), find the expected frequency for each category. d. Use a 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. Does the goodness-of-fit test suggest that the data are from a normally distributed population?

Step-by-Step Solution:

Solution 25BSC Step 1 a. The observed frequencies is given in the preceding table. 155.410-162. 162.006-168.6 Greater than Height (cm) Less than 155.410 006 01 168.601 Frequency 6 13 15 6 b. By assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, by using the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class. Now, the probability of randomly selected height belonging to each class is 0.159, 0.341, 0.341, 0.158. c. The expected frequency for each category is shown below 155.410-162. 162.006-168.6 Greater than Height (cm) Less than 155.410 006 01 168.601 Frequency 6 13 15 6 Probability 0.159 0.341 0.341 .158 Expected frequency=probabi 6.348 13.652 13.652 6.348 lity*40 d. By using = 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. We are testing Chi-square test (using EXCEL) as shown below Goodness of Fit Test expecte 2 observed (O...

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