An interactive poll found that 320 of 2,285 adults aged 18 or older have at leas

Question

An interactive poll found that 320 of 2,285 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._____ (round answer to three decimal places as needed.)

Construct the 95% confidence interval. Lower bound=_____, Upper bond=______(round answer to three decimal places as needed.) Yes or No the requirements for constructing a CI are not satisfied?____

Construct the 98% confidence interval. Lower bound=_____, Upper bond=______(round answer to three decimal places as needed.) Yes or No the requirements for constructing a CI are not satisfied?____

What is the effect of increasing the level of confidence on the width of the interval? Select the correct answer below.

Increasing the level of confidence has no effect on the interval.

Increasing the level of confidence narrows the interval.

Increasing the level of confidence widens 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 intervals in parts (b) and (c) were not met.   

Explanation / Answer

a point estimate = 320/2285 = 0.1400438

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Given a=1-0.95 = 0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n ) =0.1400438 - 1.96*sqrt(0.1400438*(1-0.1400438)/2285) =0.126

So the upper bound is

p + Z*sqrt(p*(1-p)/n ) =0.1400438 + 1.96*sqrt(0.1400438*(1-0.1400438)/2285) =0.154

Answer: No

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Given a=1-0.98= 0.02, Z(0.01) = 2.33 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n ) =0.1400438 - 2.33*sqrt(0.1400438*(1-0.1400438)/2285) =0.123

So the upper bound is

p + Z*sqrt(p*(1-p)/n ) =0.1400438 + 2.33*sqrt(0.1400438*(1-0.1400438)/2285) =0.157

Answer: No

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Increasing the level of confidence widens the interval.

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