# Confidence interval for mean

Suppose a sample of 50 is taken from a population with a standard deviation of 27 and that the sample mean is 86. Establish a 95.5% interval estimate for the population mean. Suppose, instead, that the sample size was 5000. Establish a 95.5% interval estimate for the population mean. Why might you prefer one estimate over the other?

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Please see the attachments.

Sampling

Suppose a sample of 50 is taken from a population with a standard deviation of 27 and that the sample mean is 86. Establish a 95.5% interval estimate for the population mean, Suppose, instead, that the sample size was 5000. Establish a 95.5% interval estimate for the population mean. Why might you prefer one estimate over the other?

Answer

The confidence interval is given by

Sample Size 50

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 27

Sample Mean 86

Sample Size 50

Confidence Level 95.5%

Intermediate Calculations

Standard Error of the Mean 3.818376618

Degrees of Freedom 49

t Value 2.057296743

Interval Half Width 7.855533781

Confidence Interval

Interval Lower Limit 78.14

Interval Upper Limit 93.86

Sample Size 5000

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 27

Sample Mean 86

Sample Size 5000

Confidence Level 95.5%

Intermediate Calculations

Standard Error of the Mean 0.381837662

Degrees of Freedom 4999

t Value 2.005157632

Interval Half Width 0.765644702

Confidence Interval

Interval Lower Limit 85.23

Interval Upper Limit 86.77

Thus the confidence interval is narrow when the sample size is large. Thus the second interval is preferable.

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