Question

A sample of 10 children in the 5th grade of North Stratfield School run the 100 meter dash in a average time of 29.2 seconds. Assume the bias adjusted sample standard deviation of the individual 100 meter dash times is 13.3 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? 9  

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

21.49 < μμ < 36.91

how do i get the answer for the two that are marked wrong?

Answer 1

Solution :

degrees of freedom = n - 1 = 10 - 1 = 9

t/2,df = 3.250

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

= 3.250 * ( 13.3 / 10)

Margin of error = E = 13.67

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

- E < < + E

29.2 - 13.67 < < 29.2 + 13.67

15.53 < < 42.87