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?  

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

< μμ <

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 29.2

sample standard deviation = s = 13.3

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,9 = 1.833

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

= 1.833 * (13.3 / 10)

Margin of error = E = 7.71

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

- E < < + E

29.2 - 7.71 < < 29.2 + 7.71

21.49 < < 36.91