Question

A random sample of thirty dash nine ​200-meter swims has a mean time of 3.95 minutes and the population standard deviation is 0.08 minutes. Construct a 90​% confidence interval for the population mean time. Interpret the results. The 90​% confidence interval is

Answer 1

Solution :

Given that,

= 3.95

= 0.08

n = 30

At 90% confidence level the z is ,

  = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( /n)

= 1.645 * (0.08 / 30)

= 0.024

At 90% confidence interval estimate of the population mean is,

- E < < + E

3.95 - 0.024 < < 3.95 + 0.024

3.926 < < 3.974

(3.926, 3.974)

The 90​% confidence interval is (3.926, 3.974)