Question

A random sample of thirty-six 200-meter swims has a mean time of 3.009 minutes. The population standard deviation is 0.080 minutes. A 90​% confidence interval for the population mean time is (2.987,3.031).

Construct a 90​% confidence interval for the population mean time using a population standard deviation of 0.04 minutes. Which confidence interval is​ wider? Explain.

Answer 1

The formula for estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 3.009
Z = 1.645
s_M = √(0.04²/36) = 0.007

μ = M ± Z(s_M)
μ = 3.009 ± 1.645*0.007
μ = 3.009 ± 0.0115

CI={2.998, 3.020}

Hence from the confidence interval calculation it is cear that previous confidence interval is wider.

The Z table used for Z value calculation as: