Question

1. In a poll of 592 human resource? professionals, 44.8% said that body piercings and tattoos were big grooming red flags. Complete parts? (a) through? (d) below.

**?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.

___ < P < ___

?(Round to three decimal places as? needed.)

**c)** Repeat part? (b) using a confidence level
of? 80% and rounding to three decimal places.

___ < P < ___?

**?d)** Compare the confidence intervals from
parts? (b) and? (c) and identify the interval that is wider. Why is
it? wider?

2. A study of 420,008 cell phone users found that 133 of them developed cancer of the brain or nervous system. Prior to this study of cell phone? use, the rate of such cancer was found to be 0.0411?% for those not using cell phones. Complete parts? (a) and? (b).

**a.** Use the sample data to construct a 95?%
confidence interval estimate of the percentage of cell phone users
who develop cancer of the brain or nervous system.

b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell? phones? Why or why? not?

Answer #1

Solution:-

1. Given that n = 592 , p = 0.448, q = 1-p = 1-0.448 = 0.552

b) 99% confidence interval for the proportion of the human resource = p +/- Z*sqrt(pq/n)

= 0.448 +/- 2.576*Sqrt(0.448*0.552/592)

= 0.395 , 0.501

c) 80% confidence interval for the proportion of the human resource = p +/- Z*sqrt(pq/n)

= 0.448 +/- 1.28*Sqrt(0.448*0.552/592)

= 0.422 , 0.474

d) The 99?% confidence interval is wider than the 80?% confidence interval. As the confidence interval? widens, the probability that the confidence interval actually does contain the population parameter increases.

2) p = 133/420008 = 0.0003166, q = 1- 0.0003166 = 0.9996834

a. 95% confidence interval estimate of the percentage of cell phone

= 0.0003166 +/- 1.96*sqrt(0.0003166* 0.9996834/420008)

= 0.0002628 , 0.0003704

= 0.02628%, 0.03704%

b. No, because 0.0411?% is included in the confidence interval.

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