A research group conducted an extensive survey of 2975 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?" 1608 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

90% Confidence interval for population proportion = (0.526, 0.556)

Lower limit of the 90% confidence interval for population proportion of all wage and salaried workers who would respond the same way to the stated question = 0.526

Upper limit of the 90% confidence interval for population proportion of all wage and salaried workers who would respond the same way to the stated question = 0.556

Step-by-step explanation:

- Extensive survey is carried out on 2975 wage and salaried workers on issues ranging from relationships with their bosses to household chores.

- 1608 responded, "Personal satisfaction from doing a good job."

p is 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.

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (1608) ÷ (2975) = 0.5405

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 90% confidence interval for sample size of 2975 is obtained from the z-tables. (Large enough sample size)

Critical value = 1.645

standard Error will be calculated thus

Standard error = σₓ = √[p(1-p)/n]

p = 0.5405

n = sample size = 2975

σₓ = √[0.5405×0.4595/2975] = 0.0091368632

σₓ = 0.009137

90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.5405 ± (1.645 × 0.009137)

CI = 0.5405 ± 0.015030365

CI = 0.5405 ± 0.0150

90% CI = (0.5255, 0.5555)

90% Confidence interval = (0.526, 0.556)

Hope this Helps!!!

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2