Question

A random sample of fifty-two ​200-meter swims has a mean time of 3.59 minutes and the population standard deviation is 0.08 minutes. Construct a 95​% confidence interval for the population mean time. Interpret the results.

The 95​% confidence interval is ( ____ , ____ ) (Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

= 3.59

= 0.08

n = 52

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 =1.96

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

= 1.96 * (0.08 / 52)

= 0.02

At 95% confidence interval estimate of the population mean is,

- E < < + E

3.59 - 0.02 < < 3.59 - 0.02

3.57 < < 3.61

The 95% confidence interval is (3.57, 3.61)

We are 95% confidence that a mean time will come in between interval (3.57, 3.61)