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Thirty-five people from a random sample of 125 workers from Company A admitted to using
Chapter 10, Problem t10.2(choose chapter or problem)
Section I: Multiple Choice Select the best answer for each question.
Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren’t really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren’t ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren’t ill is
(a) \(0.03 \pm \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(b) \(0.03 \pm 1.96 \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(c) \(0.03 \pm 1.645 \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(d) \(0.03 \pm 1.96 \sqrt{\frac{(0.269)(0.731)}{125}+\frac{(0.269)(0.731)}{68}}\)
(e) \(0.03 \pm 1.645 \sqrt{\frac{(0.269)(0.731)}{125}+\frac{(0.269)(0.731)}{68}}\)
Questions & Answers
QUESTION:
Section I: Multiple Choice Select the best answer for each question.
Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren’t really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren’t ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren’t ill is
(a) \(0.03 \pm \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(b) \(0.03 \pm 1.96 \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(c) \(0.03 \pm 1.645 \sqrt{\frac{(0.28)(0.72)}{125}+\frac{(0.25)(0.75)}{68}}\)
(d) \(0.03 \pm 1.96 \sqrt{\frac{(0.269)(0.731)}{125}+\frac{(0.269)(0.731)}{68}}\)
(e) \(0.03 \pm 1.645 \sqrt{\frac{(0.269)(0.731)}{125}+\frac{(0.269)(0.731)}{68}}\)
ANSWER:Step 1 of 2
Given,
The workers from Company A,
The workers from Company B,
The proportion of workers from Company A admitted that they had used sick leave when they weren’t ill,
The proportion of workers from Company B admitted that they had used sick leave when they weren’t ill,
We have to determine the 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they were not ill.