Question

) A study is conducted in a company that employs 800 engineers. A random sample of 50 engineers reveals that the average sample age is 34.3 years. Historically, the population standard deviation of the age of the company’s engineers is approximately 8 years. Construct a 98% confidence interval to estimate the average age of all the engineers in this
company.

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Answer 1

Answer:

8% confidence interval to estimate the average age of all the engineers in this company = (31.66,36.94)

Explanation:

Number of engineers employed(n) = 800

Average sample age (x) = 34.3 years

the population standard deviation of the age of the company’s engineers (y) = 8 years

Two- sided confidence interval is ;

CI = ( x-((z × y)/√n), x+((z × y)/√n))

for 98% confidence α = 1 - 0.98

                                 α = 0.02

α / 2 = 0.02 / 2 = 0.01

z = z(0.01) = 2.33

CI = ( 34.3 - (2.33 × 8) / √800, 34.3 + (2.33 × 8) / √800)

    = (34.3- 2.64, 34.3 + 2.64)

    = (31.66,36.94)

Therefore 98% confidence interval to estimate the average age of all the engineers in the company is (31.66,36.94)

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