Question

a random sample of 38 200 meter swims by a mean time of 3.98 minutes and the population standard deviation is 0.08 minutes. Construct a 90% interval for the population mean time. interpret results

Answer 1

n = sample size = 38

= sample mean = 3.98

= population SD = 0.08

SE = / = 0.08/ = 0.0130

= 0.10

From Table, critical value of Z = 1.645

90% Confidence interval:

Z SE

= 3.98 1.645 X 0.0130

= 3.98 0.0213

= ( 3.9587, 4.0013)

Interpretation:

The 90% confidence interval (3.9587,4.0013) defines a range of values that we can be 90% certain contains the population mean .