Question

In: Statistics and Probability

A research group conducted an extensive survey of 3058 wage and salaried workers on issues ranging...

A research group conducted an extensive survey of 3058 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?" 1469 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    

Solutions

Expert Solution

Solution :

Given that,

n = 3058

x = 1469

Point estimate = sample proportion = = x / n = 1469/3058=0.480

1 - = 1-0.480=0.520

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 (((0.480*0.520) / 3058)

E = 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.480 - 0.015< p <0.480+ 0.015

0.465< p < 0.495

The 90% confidence interval for the population proportion p is : lower limit=0.465,upper limit =0.495


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