Explanation Given info: The data represents the average hours worked per week and the numbers of on-the-job injuries for a random sample of U.S companies in a recent year. Also, α = 0.05 . Calculation: Here, the claim is that “there is a significant correlation between average hours worked and the number of on-the-job injuries”. State the hypotheses: The test hypotheses are given below: Null hypothesis: H 0 : There is no correlation between average hours worked and the number of on-the-job injuries. Alternative hypothesis: H a : There is correlation between average hours worked and the number of on-the-job injuries. Critical value: If the sample size n is greater than 30 then the formula for critical value is, ± z n − 1 , z corresponds to the level of significance From the information the sample size n is 35 and α = 0.05 . From Standard normal, the critical value at α = 0.05 is 1.96. Substitute 1.96 for ± z , 33 for n in the critical value formula. Critical value = ± 1.960 33 − 1 = ± 1.96 32 = ± 1.96 5.6569 = ± 0.3465 Thus, the critical value is ±0.3465. Test Statistic: r s = 1 − 6 ∑ d 2 n ( n 2 − 1 ) Here, ∑ d 2 is the sum of squares of the differences of the ranks of the data sets and n is the sample size. For repeated values, to give rank take the average for the succeeding ranks of those values. Hours worked Rank Injuries Rank d d 2 38 24.5 11 24 ( 24.5 − 24 ) = 0.5 0.25 38 24.5 11 24 0.5 0.25 37 30.5 9 28 2.5 6.25 38 24.5 10 26.5 –2 4 38 24.5 10 26.5 –2 4 40 13.5 17 11.5 2 4 39 18 15 15.5 2.5 6.25 39 18 14 17.5 0.5 0.25 39 18 14 17.5 0.5 0.25 40 13.5 16 14 –0.5 0.25 39 18 15 15.5 2.5 6.25 41 9 17 11.5 –2.5 6.25 41 9 17 11.5 -2.5 6.25 42 3 21 3 0 0 41 9 18 7.5 1.5 2.25 41 9 18 7

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Author: Larson

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Chapter 11.4, Problem 14E

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To check: Whether there is a significance correlation between average hours worked and the number of on-the-job injuries.

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Chapter 11.4, Problem 13E

Chapter 11.5, Problem 1TY

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In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.

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To check: Whether there is a significance correlation between average hours worked and the number of on-the-job injuries.

Solution Summary: The author concludes that there is a significant correlation between average hours worked and the number of on-the-job injuries.

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To check: Whether there is a significance correlation between average hours worked and the number of on-the-job injuries.

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Chapter 11 Solutions