Question

In: Statistics and Probability

Sun Blush Technologies is a well established company with thousands of employees and they want to...

Sun Blush Technologies is a well established company with thousands of employees and they want to estimate the average age of their workers. A sample of 97 employees was taken. Assuming the population has a standard deviation of 7.8, we want to find a 90% confidence interval for the population mean. If the mean of the sample is 34.2, what is the confidence interval estimate? For full marks your answer should be accurate to at least two decimal places.

Expert Solution

Solution

Given that,

= 34.2

= 7.8

n = 97

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2* ( $\sqrt$ /n)

= 1.645* (7.8/ $\sqrt$ 97 )

= 1.30

At 90% confidence interval estimate of the population mean is,

- E < < + E

34.2 - 1.30 < < 34.2 + 1.30

32.90 < < 35.50

(32.90 , 35.50)

orchestra answered 1 year ago

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