Question

A sample of 14 children in the 5th grade of North Stratfield School run the 100 meter dash in a average time of 26.2 seconds. Assume the bias adjusted sample standard deviation of the individual 100 meter dash times is 9 seconds.
Construct a 99% confidence interval for μμ, the true population mean 100 meter dash time. Since n is small, the t statistic will be used in deriving this confidence interval.
What is the degrees of freedom parameter that should be used to derive the t-value? ______

What is the confidence interval? Give your answers as decimals, to two places

________ < μμ < ________

Answer 1

Solution :

degrees of freedom = 14 - 1 = 13

t _/2,df = 3.012

Margin of error = E = t_/2,df * (s /n)

= 3.012 * (9 / 14)

Margin of error = E = 7.27

The 99% confidence interval estimate of the population mean is,

- E < < + E

26.2 - 7.27 < < 26.2 + 7.27

18.93 < < 33.47