Use the following sample to estimate a population mean .

Question

Use the following sample to estimate a population mean �.

51.8

64.9

59.8

55.6

57.9

71

58.7

Assuming the population has a bell-shaped distribution, find the 95% confidence interval about the population mean. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places.



Answer 1

First find the mean and standard deviation. Sample mean = 59.957; Sample standard deviation = 6.295.

Then we need the critical value for the 95% confidence interval. Since we have only 7 data points and we don't know the population variance, we need to use a student T distribution with 6 degrees of freedom. This gives us the critical value of 2.447.

The Margin of Error is equal to the critical value times the standard deviation divided by the square root of n.

MOE = ^2.447*6.295/_√7 = 5.8216

For the confidence interval, simply add and subtract this margin of error from the sample mean.

(54.136, 65.779)