An interactive poll found that 350 of 2393 adults aged 18 or

An interactive poll found that 350 of 2,393 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 98% 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?

Solution

a)
No.of Having atleast one tatto(x)=350
Sample Size(n)=2393
Sample proportion = x/n =0.146
b)
Confidence Interval For Proportion
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 = [ 0.146 ±Z a/2 ( Sqrt ( 0.146*0.854) /2393)]
= [ 0.146 - 1.96* Sqrt(0) , 0.146 + 1.96* Sqrt(0) ]
= [ 0.132,0.16]
c)

Confidence Interval = [ 0.146 ±Z a/2 ( Sqrt ( 0.146*0.854) /2393)]
= [ 0.146 - 2.33* Sqrt(0) , 0.146 + 2.33* Sqrt(0) ]
= [ 0.129,0.163]

d)
Increase the confidence widen the interval