An interactive poll found that 382 of 2286 adults aged 18 or

An interactive poll found that 382 of 2,286 adults aged 18 or older have at least 1 tattoo. A.) obtain a point estimate for the proportion of adults who have at least 1 tattoo. B.) Construct a 90% confidence interval for the proportion of adults with at least 1 tattoo. Upper and lower bounds. C.) Construct a 99% confidence interval for the proportion of adults with at least 1 tattoo. D.) What is the effect of increasing the level of confidence on the width of the interval?

Solution

A.
Mean(x)=382
Sample Size(n)=2286
Sample proportion = x/n =0.167
B. AT 95% C.I
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval

Confidence Interval = [ 0.167 ±Z a/2 ( Sqrt ( 0.167*0.833) /2286)]
= [ 0.167 - 1.64* Sqrt(0) , 0.167 + 1.64* Sqrt(0) ]
= [ 0.154,0.18]
C)
AT 99% C.I

Confidence Interval = [ 0.167 ±Z a/2 ( Sqrt ( 0.167*0.833) /2286)]
= [ 0.167 - 2.58* Sqrt(0) , 0.167 + 2.58* Sqrt(0) ]
= [ 0.147,0.187]

D)
It is increased, 0.7% change in interval