Question

In a random sample of five microwave​ ovens, the mean repair cost was​$75.00 and the standard deviation was ​$12.50

Assume the population is normally distributed and use a​ t-distribution to construct a 90​% confidence interval for the population mean u

What is the margin of error of μ​?

Interpret the results.

Answer 1

Given:

Sample size = n = 5 Sample mean = Sample standard deviation = s = 12.50   

Assuming that the population is normally distributed, 90% confidence interval for the population mean can be constructed using the formula:

can be obtained from t tables for = 0.10 / 2 = 0.05 and n - 1 = 5 - 1 = 4 df

Substituting in the formula,

90% confidence interval for the population mean

=

90% confidence interval for the population mean is obtained as

The margin of error of =

It implies that we are 90% confidennt that the true population mean would lie in this interval. If 100 additional samples are drawn, then the true population mean will fall in the interval 90 out of 100 times.