Question

An interactive poll found that 386 of 2 comma 324 adults aged 18 or older have at least one tattoo. ?(a) Obtain a point estimate for the proportion of adults who have at least one tattoo. ?(b) Construct a 95?% confidence interval for the proportion of adults with at least one tattoo. ?(c) Construct a 98?% confidence interval for the proportion of adults with at least one tattoo. ?(d) What is the effect of increasing the level of confidence on the width of the? interval?

Answer 1

Soln

Given that Proportion of adult aged 18 or older

a) Hence the point estimate for the porprtion can be calculated as

and also proportion of adult not aged 18 or less

Now according to question

b) At 95 % Confidence level The confidence interval can be written as

CI=

where E can be calculated as

Z_c=1.96 at 95 % confidence level.

So, CI of population proportion

0.0151<<0.181

c) Simillarly at 98 % confidence level similar formulae will be used but value of Z_c will be changed as

Z_c= 2.33 so,

Now Confidence Interval

d) Here while compare the both Confidence interval at different confidence level we can see that as we increase our confidence level it is evident that Interval also increases and vice versa.