Question

A study of 420 comma 059 cell phone users found that 130 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 0.0438​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

2. Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 934 and x equals 524 who said​ "yes." Use a 95 % confidence level. ​b) Identify the value of the margin of error E.

Answer 1

1)

A study of 420 comma 059 cell phone users found that 130 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 0.0438​% for those not using cell phones. Complete parts​ (a) and​(b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

Answer)

Po = 0.000438

N = 420059

P = 130/420059

First we need to check the conditions of normality that is if n*po and n*(1-po) both are greater than 5 or not

N*po = 184.073442

N*(1-po) = 420074.926558

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 90% confidence level is 1.645

Margin of error (MOE) = Z*√{Po*(1-Po)}/√N

After substitution

MOE = 0.00005309447304

Confidence interval is given by

P-MOE < P < P+MOE

0.00025638586 < P < 0.00036257480

In percentage

0.0256 < P < 0.0363