In: Statistics and Probability
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 iswider? Explain.
Solution :
Given that,
n = 56
At 95% confidence level the z is ,
Margin of error = E = Z/2* ( /n)
= 0.013
At 95% confidence interval estimate of the population mean is,
3.121 - 0.013 < < 3.121 + 0.013
(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