A research group conducted an extensive survey of 2867 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?" 1563 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)
lower limit
upper limit
Answer:
Given,
sample n = 2867
x = 1563
p^ = x/n
= 1563/2867
= 0.5452
= 0.55
Here at 90% CI, z value is 1.645
Consider,
Interval = p^ +/- z*sqrt(p^(1-p^)/n)
substitute values
= 0.55 +/- 1.645*sqrt(0.55(1-0.55)/2867)
= 0.55 +/- 0.0153
= (0.5347 , 0.5653)
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