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, q, known to be 13. the sample mean, x, is found to be 108.

A) Compare the 96% confidence interval about u if the sample size, n, is 25.

B) Compute the 96% confidence interval about u if the sample size, n, is 10. How does decreasing the sample size affect the margin of error,E?

C) Compare the 88% confidence interval about u if the sample size, n, is 25. 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?

Explanation / Answer

A)

Z = 2.05

A 96% Confidence interval with n = 25 is given by:

CI is 108 +/- 2.05*13/sqrt(25)
=102.67 to 113.33

B) A 96% Confidence interval with n = 25 is given by:

Z = 2.05

CI is 108 +/- 2.05*13/sqrt(10)

=77.573 to 116.428

C) Z = 1.555 is the confidence level

Hence,

CI is 108 +/- 1.556*13/sqrt(25)

=103.95 to 112;05

So, compared to A this is a smaller confidence level. When the sample size is same, and a higher confidence is being asked then the range of values increases. If confidence level asked is lower, then we can get the population mean in a much smaller range.

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