n interactive poll tound that 376 of 2,265 adults aged 18 or older have at least
ID: 3054687 • Letter: N
Question
n interactive poll tound that 376 of 2,265 adults aged 18 or older have at least one tattoo. (a) Obtain a point estimate for the proportion af aduts who have at least one tattoo. (b) Construct a 90% condence interval for the proportion of adults with at least one tattoo. (c) Construct a 9996 confidence interval for the proportion of adults with at least one tattoo (d) What is the efect of increasing the level of confidence on the width of the interval? (a) Round to three decimal places as needed) (b) Construct the 90% confidence interval. Select the correct choice below and, t necessary, il in the answer boxes to complete your chaice O A. Lower bound Upper bound Round to three decimal places as needed.) O B. The requrements for constructing a confidence interval are not satisfied (c) Construct the 99% cntdence interval select the correct eace below and, i necessary, fi in the answer baies so complese your choose O A. Lower bound Upper bound Round to three decimal places as needed) Cick to select your answers) 0Explanation / Answer
Ans:
a)point estimate=sample proportion=376/2265=0.166
b)z value for 90% CI is 1.645
90% confidence for population proportion is
=0.166+/-1.645*sqrt(0.166*(1-0.166)/2265)
=0.166+/-0.013
=(0.153, 0.179)
c)z value for 99% CI is 2.58
99% CI for population proportion is
=0.166+/-2.58*sqrt(0.166*(1-0.166)/2265)
=0.166+/-0.020
=(0.146, 0.186)
d)As,the conidence level increases,z multiplier value increases,so margin of error increases,hence width of CI will increase.
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