Question

A random sample of fifty -six 200-meter swims has a mean time of 3.121 minutes. The population standard deviation is 0.080 minutes. A 95​% confidence interval for the population mean time is (3.103,3.139).

Construct a 95​% confidence interval for the population mean time using a population standard deviation of 0.05 minutes. Which confidence interval is​wider? Explain.

Answer 1

Solution :

Given that,

= 3.121

= 0.05

n = 56

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.005 = 1.96

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

= 1.96 * (0.05 / 56)

= 0.013

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

- E < < + E

3.121 - 0.013 < < 3.121 + 0.013

3.108 < < 3.134

(3.108, 3.134)

The confidence interval (3.103,3.139) is ​wider beacuse margin of error (0.020) is greater for standard deviation 0.080 than for 0.05