Explanation Given info: The data represents the number of success and failures for three categories of variables. Calculation: The test hypotheses are given below: Null hypothesis: H 0 : p 1 = p 2 = p 3 Alternative hypothesis: H 1 : At least one of the proportions is different from others. Decision rule: If χ 0 2 > χ α 2 , then reject the null hypothesis. Test statistic: The row and column total is obtained below: Category 1 Category 2 Category 3 Total Success 204 199 214 617 Failure 96 121 98 315 Total 300 320 312 932 Expected count: The formula for expected count is given below: ( row total ) ( column total ) ( table total ) The expected count for each category is tabulated below: Category 1 Category 2 Category 3 Success 617 × 300 932 = 198.605 617 × 320 932 = 211.845 617 × 312 932 = 206 .549 Failure 315 × 300 932 = 101 .395 315 × 320 932 = 108.155 315 × 312 932 = 105 .451 The requirements that must be satisfied to perform the test are, All the expected frequencies are greater than or equal to 1. That is, all E i ≥ 1 where E i represents the expected counts of category i. Not more than 20% of the expected frequencies are less than 5. From the table, it can be observed that none of the expected frequency is less than 5. Therefore, the requirement of the test is satisfied. The value of the test statistic is, χ 0 2 = ∑ ( O i − E i ) 2 E i = { ( 204 − 198

Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134508306

Author: Michael Sullivan III

Publisher: PEARSON

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 12.2, Problem 6AYU

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To test: Whether the proportions are equal for each category at the α=0.01 level of significance.

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Chapter 12.2, Problem 5AYU

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Chapter 12 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYU Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...

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To test: Whether the proportions are equal for each category at the α = 0.01 level of significance.

Solution Summary: The author explains that there is not enough evidence to infer that at least one of the proportions is different from others at alpha =0.01 level of significance.

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To test: Whether the proportions are equal for each category at the α=0.01 level of significance.

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Chapter 12 Solutions