Question

In a poll of 555 human resource professionals, 40.0% said that body peircings and tattoos were big grooming red flags. Complete parts (a) through (d)

a.) among the 554 human resource professionals who were surveyed, how many of them said that the body piercings and tattoos were big grooming red flags ?

b.) construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags

< p <

c.) repeat part (b) using a confidence level of 80%

< p <

d.) compare the confidence intervals from parts b and c what identify the interval that is wider. Why is it wider ?

Answer 1

Part a)

n = 554

40.0% said that body peircings and tattoos were big grooming red flags

554 * 40.0% = 221.6 222

222 said that body piercings and tattoos were big grooming red flags

Part b)

n = 555



Lower Limit =
upper Limit =
99% Confidence interval is ( 0.3464 , 0.4536 )
( 0.3464 < P < 0.4536 )

Part c)

n = 555



Lower Limit =
upper Limit =
80% Confidence interval is ( 0.3733 , 0.4267 )
( 0.3733 < P < 0.4267 )

Part d)

Calculating width of confidence interval

99% Confidence interval is ( 0.3464 , 0.4536 ) = 0.4536 - 0.3464 = 0.1072

80% Confidence interval is ( 0.3733 , 0.4267 ) = 0.4267 - 0.3733 = 0.0534

WE can see that 99% CI is wider than 80 CI as critical value increases from 80% to 99%

   for 99%

for 80%