Use the sample data and confidence level given below to complete parts (a) throu

Question

Use the sample data and confidence level given below to complete parts (a) through (d) Aresearch isiile pol asked iespordertsttey kn vunerate bidrity then he pou n-1015 and X-S12 who sad 'es ubeagg% annence evel Click the icon to view a table of z scores a) Find the best point estimate of the population proportion p (Hound to three decimal places as needed ) b) Identty the value of the margin of enor E Round to three decmal places as needed ) c) Construct the confidence interval (Round to treee decimal places as needed.) d) wirite a statement that comectihy interprets the confidence interval. Choose the cormect answer below A. OB. Oe. OD. One has 99% confidence that the sample proponlin is equal to the populaon propodn dne has 99% condence that the iterval from the ower bound to the upper bound actuary does cotan te true vate oftepopulation proportion There ts a 99% ctance tat te tue vabe of the population proportion wu tall between e lower bound and the upper bound 9%0f sample proportions will tai between the lower tound and the upper bound Click to select your answers) Type here to search

Explanation / Answer

a)

p = 512/1015 = 0.5044

b)

n = 1015

p = 0.5044

z-value of 99% CI = 2.5758

SE = sqrt(p*(1-p)/n)

= sqrt(0.5044*(1-0.5044)/1015)

= 0.01569

Margin of error, ME = z*SE

= 2.5758*0.01569

= 0.04042

c)

Lower Limit = p - ME = 0.5044 - 0.04042 = 0.46401

Upper Limit = p + ME = 0.5044 - 0.04042 = 0.54486

99% CI (0.464 , 0.545)

d)

Option C

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