Question

(1 point) Working backwards, Part I. A 90% confidence interval for a population mean is (44, 50). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 28 observations. Calculate the sample mean, the margin of error, and the sample standard deviation. Use the t distribution in any calculations. Round non-integer results to 4 decimal places.

Sample mean =

Margin of error =

Sample standard deviation =

Answer 1

Solution:

We are given

Lower limit = 44

Upper limit = 50

Confidence level = 90%

n = 28

df = n - 1 = 27

Critical t value = 1.703288

Sample mean = (Upper limit + lower limit) / 2 = (50 + 44)/2 = 47

Margin of error = (Upper limit - lower limit) / 2 = (50 - 44)/2 = 3

Standard deviation = Margin of error * Sqrt(n) / t

Standard deviation = 3*sqrt(28)/ 1.703288

Standard deviation = 9.31992

Sample mean = 47

Margin of error = 3

Sample standard deviation = 9.32