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# Confidence interval for mean

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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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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?
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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