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# Estimates and Sample Sizes - Stats

You can use StatCrunch or the appropriate equations for calculating the confidence intervals.

I. A personnel manager at a large firm needs to estimate the mean length of stay, ? of its employees. She takes a random sample of employees and finds the sample mean (?x) to be 25 years.

a) Use the above data, ?x = 25, to find a 90% confidence interval for ? if the employee sample size is 64, and a known population standard deviation ? = 16.

What is the appropriate distribution (z or t)? ___________

b) What is its numerical value (obtain answer from the appropriate table, z or t?
___________

c) What is the Confidence Interval? (Provide answer to at least two decimal places)

________________________ ________________________

II. Find a 95% Confidence Interval for the mean length of stay (?) of the employees of the large company if the point estimate for µ is?x =25, the sample size is 9 and the sample standard deviation s = 12. (You can assume the distribution is normal).

a) What is the appropriate distribution (z or t)? ___________

b) What is its numerical value (obtain answer from the appropriate table, z or t?
___________

c) What is the Confidence Interval? (Provide answer to at least two decimal places.)

________________________ ________________________.

#### Solution Preview

Please refer to the attachment for the full solution.

Problem-I: A personnel manager at a large firm needs to estimate the mean length of stay of its employees. She takes a random sample of employees and finds the sample mean (x) to be 25 years. Use the above data, x = 25, to find a 90% confidence interval for µ. If the employee sample size is 64, and a known population standard deviation σ = ...

#### Solution Summary

The solution provides step-by-step answers that estimates and provides sample sizes in the given statistics questions given.

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