Question

A random sample of 47

two hundred meter swims* has a mean time of 3.99 minutes and the population standard deviation is 0.09 minutes.

*construct a ninety percent confidence interval for the population mean time. Interpret the results. The 90% confidence interval is___, ____.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.99

Population standard deviation = = 0.09

Sample size = n = 47

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 * (0.09 / 47)

= 0.02

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

- E < < + E

3.99 - 0.02 < < 3.99 + 0.02

3.97 < < 4.01

(3.97 , 4.01 )