In a poll of 542 human resourceprofessionals 417 said that b

In a poll of 542 human resourceprofessionals, 41.7% said that body piercings and tattoos were big grooming red flags. Complete parts(a) through(c) below. a) Among the 542 human resource professionals who weresurveyed, how many of them said that body piercings and tattoos were big grooming redflags? 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. c) Repeat part(b) using a confidence level of 80%.

Solution

a)
It is given 41.7% said that body piercings and tattoos were big grooming redflags

41.7% sample size is = 0.417 * 542 = 226.014 ~ 226   

b)
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

Sample proportion = x/n =0.417
Confidence Interval = [ 0.417 ±Z a/2 ( Sqrt ( 0.417*0.583) /542)]
= [ 0.417 - 2.58* Sqrt(0) , 0.417 + 2.58* Sqrt(0) ]
= [ 0.362,0.472]

c)
WHEN C.I is 80%
Confidence Interval = [ 0.417 ±Z a/2 ( Sqrt ( 0.417*0.583) /542)]
= [ 0.417 - 1.28* Sqrt(0) , 0.417 + 1.28* Sqrt(0) ]
= [ 0.39,0.444]