Explanation Given info: The data represents Gestational period in weeks and the level of education of the baby. Calculation: The test hypotheses are given below: Null hypothesis: H 0 : Gestation period and completing high school are independent. Alternative hypothesis: H 1 : Gestation period and completing high school are not independent. Decision rule: If χ 0 2 > χ α 2 , then reject the null hypothesis. Test statistic: The row and column total is calculated below: Less than high school degree Gestational period 22-27 28-32 33-36 37-42 43+ Total Yes 14 34 140 1010 81 1279 No 26 65 343 3032 208 3674 Total 40 99 483 4042 289 4953 Expected count: The formula for the expected count is given below: ( row total ) ( column total ) ( table total ) The expected count for each category is tabulated below: Less than high school degree Gestational period 22-27 28-32 33-36 37-42 43+ Yes 1 , 279 × 40 4 , 953 = 10.329 1 , 279 × 99 4 , 953 = 25.565 1 , 279 × 483 4 , 953 = 124.724 1 , 279 × 4 , 042 4 , 953 = 1043.755 1 , 279 × 289 289 = 74.628 No 3 , 674 × 40 4953 = 29.671 3 , 674 × 99 4 , 953 = 73.435 3 , 674 × 483 4 , 953 = 358.276 3 , 674 × 4 , 042 4 , 953 = 2 , 998.245 3 , 674 × 289 4 , 953 = 214.372 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 frequencies are less than 1

Fundamentals of Statistics, Books a la Carte Edition Plus MyLab Statistics with Pearson eText -- Access Card Package (5th Edition)

5th Edition

ISBN: 9780134763699

Author: Michael Sullivan III

Publisher: PEARSON

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Chapter 12, Problem 4RE

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To test: Whether gestation period and completing high school are independent at the α=0.05 level of significance.

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Chapter 12, Problem 3RE

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Fundamentals of Statistics, Books a la Carte Edition Plus MyLab Statistics with Pearson eText -- Access Card Package (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 gestation period and completing high school are independent at the α = 0.05 level of significance.

Solution Summary: The author evaluates whether gestation period and completing high school are independent at the alpha =0.05 level of significance.

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