Question

# A research group conducted an extensive survey of 2872 wage and salaried workers on issues ranging...

A research group conducted an extensive survey of 2872 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?" 1553 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

Solution :

Given that,

Point estimate = sample proportion = = x / n = 1553 / 2872 = 0.541

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.541 * 0.459) / 2872)

= 0.016

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.541 - 0.016 < p < 0.541 + 0.016

0.525 < p < 0.557

(0.525 , 0.557)

Lower limit = 0.525

Upper limit = 0.557

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