A research group conducted an extensive survey of 3037 wage and salaried workers

Question

A research group conducted an extensive survey of 3037 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "what does success mean to you? 1527 responded, Personal satis action rom doing a good job. Let be the population proportion of all age and talaned workeriho would res odde we wto theatedoene. Ho ile ge , wet isneeded f we wsh to be 95% confiden that the sample centage of those equating success with personal satisfaction is wen i 9% of the population percentage, (int use p .0 50 as a 1mnary estimate. Round your answer up to the nearest whole number) workers Three-circle, red-on-white is one distinctive patterm painted on ceramic vessels of the Anasazi period found at an archaeological site. At one excavation, a sample of 163 potsherds indicated that 70 were of the three-circle, red-on-white pattern (o) Find a point estimate # for the proportion of all ceramic potsherds at chis ste that are of the three-circle, red-on-white partem. (Round your answver to four decimal 4204 (b) Compute a 95% confidence interval for the population proponen of all cranic potsherds ith tha dit decimal places) lower limit 3900 upper limit 4082 ctive pattern ford at the .t. Rund ve nant

Explanation / Answer

10)

p=1527/3037 =0.5028

q=1-p

=1-0.5028

=0.4972

Margin of error,E =Z/2 × [(p×q)/n]

0.019 =1.96 x [(0.5028*0.4972)/n]

0.019 =1.96 x0.4999/n

0.019 =0.97998 /n

n =0.97998/0.019

n =51.578

n=51.578^2

n=2661

11)

a) p=70/163 =0.4294

q=1-p =1-0.4294 =0.5706

b) CI = p ± Z/2 × [(p×q)/n]

               =0.4294 ± 1.96 x(0.4294*0.5706/163)

               =0.4294 ±0.0760

              

lower limit =0.4294-0.076

               =0.353

upper limit =0.4294+0.076

               =0.505

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