a simple random sample of size n is drawn from a population that is normally dis

Question

a simple random sample of size n is drawn from a population that is normally distributed with population standard deviation known to be 17. The sample mean is found to be 123.

a. Compute the 94% confidence interval about u (meu) if the sample size n is 20.

b. compute the 94% confidence interval for u if the sample size n is 12. How does decreasing the level of confidence affect the size of the margin of error, E?

c. Compute the 85% confidence interval for u if the sample size n is 20. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?

d. Could we have computed the confidence intervals in parts a-c if the population had not been normally distributed?Why?

e. If an analysis of the sample data revealed one outlier grater than the mean, how would this affect the confidence interval?

Explanation / Answer

µ = population mean

= population standard deviation

x= sample mean

n = number of sample values

E = margin of error

z/2 = z score separating an area of a/2 in the right tail of the standard normal distribution

Confidence Interval for Estimating a Population Mean (with Known) Definition The two values

x – E and x + E are called confidence interval limits.

where E=z/2./n^(1/2)

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