Question: Given a sample size of n = 225. Let the variance of the population be 2 = 8.41. Let the mean of the sample be

Given a sample size of n = 225. Let the variance of the population be ² = 8.41. Let the mean of the sample be xbar = 12. Construct a 99% confidence interval for , the mean of the population, using this data and the central limit theorem.

a.What is the standard deviation of the mean xbar of sample size n, i.e. what is _xbar , in terms of and n?

b.Is this a one-sided or two-sided problem?

c.What value of z should be used in computing k, the margin of error, where

z = k/_xbar= k/[/]?

d.What is k?

e.Write the 99% confidence interval for based on xbar and k,

(xbar - k) < < (xbar + k)

f.Using the Z-score applet "Area from a value". Let the Mean = 12, and SD = _xbar. Choose "Between (xbar -k) and (xbar + k)" using xbar = 12 and your computed value of k. Hit "Recalculate". Does the probability approximately equal 0.99? (yes or no). Include a screen shot of your answer.

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