In a poll of 589 human resource professionals, 46.7% said that body piercings an

Question

In a poll of 589 human resource professionals, 46.7% said that body piercings and tattoos were big grooming red flags. Complete parts (a) through (d) below. a) Among the 589 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big grooming red flags? b) Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags. c) Repeat part (b) using a confidence level of 80%. Compare the confidence intervals from parts (b) and (c) and identify the interval that is wider. Why is it wider? d) Select the correct choice below and fill in the answer boxes to complete your choice.

Explanation / Answer

(a) Expected number of human resource professional who said the body piercings and tattoos were big grooming red flags = 589 * 46.7/100 = 275.1 or say 275

(b) Here confidence interval = 99%

99% confidence interval = p^ +- Z99% sqrt [p^(1-p^)/ N]

here p^ = 0.467 ; Z99% = 2.575 and N = 589

90% confidence interval = p^ +- Z90% sqrt [p^(1-p^)/ N] = 0.467 +- 2.575 * sqrt [0.467 * 0.533/589]

= 0.467 +- 0.053

= (0.414, 0.520)

(c) Here confidence interval = 80%

99% confidence interval = p^ +- Z80% sqrt [p^(1-p^)/ N]

here p^ = 0.467 ; Z80% = 2.575 and N = 589

90% confidence interval = p^ +- Z90% sqrt [p^(1-p^)/ N] = 0.467 +- 1.28* sqrt [0.467 * 0.533/589]

= 0.467 +- 0.026

= (0.441, 0.493)

(d) We can see that the 99% confidence interval is way wider than 80% confidence ineterval. It is wider because it make 99% probability and the other one only 80% probability.

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