An interactive poll found that 309 of 2, 352 adults aged 18 or older have at lea

Question

An interactive poll found that 309 of 2, 352 adults aged 18 or older have at least one tattoo. Obtain a point estimate for the proportion of adults who have at least one tattoo. Construct a 95% confidence interval for the proportion of adults with at least one tattoo. Construct a 99% confidence interval for the proportion of adults with at least one tattoo. What is the effect of increasing the level of confidence on the width of the interval? P (Round to three decimal places as needed.) Construct the 95% confidence interval. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. Lower bound: Upper bound: (Round to three decimal places as needed.) The requirements for constructing a confidence interval are not satisfied. Construct the 99% confidence interval. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. Lower bound: Upper bound: (Round to three decimal places as needed.) The requirements for constructing a confidence interval are not satisfied. Choose the correct answer below. Increasing the level of confidence narrows the interval. Increasing the level of confidence widens the interval. Increasing the level of confidence has no effect on the interval. It is not possible to tell the effect of increasing the level of confidence on the width of the interval since the requirements for constructing a confidence interval in parts (b) and (c) were not met.

Explanation / Answer

a) p=309/2352=0.1314

b) std error =(p(1-p)/n)1/2 =0.007

for 95% CI, z=1.96

hence confidence interval=mean +/- z*std error =0.118 ; 0.145

c) for 99% CI, z =2.5758

hence confidence interval=mean +/- z*std error =0.113 ; 0.149

d)option B is correct

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