Question

Working backwards, Part I. A 90% confidence interval for a population mean is (82, 92). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 24 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.

Answer 1

Solution :

Given that,

Lower confidence interval = 82

Upper confidence interval = 92

  = (Lower confidence interval + Upper confidence interval ) / 2

= (82 + 92) / 2

= 87

Margin of error = E = Upper confidence interval -   = 92 - 87 = 5

Margin of error = 5

sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

t _/2,df = t_0.05,23 = 1.714

s = E * n / t_/2,df = 5 * 24 / 1.714 = 14.2910

sample standard deviation = 14.2910