Question

If n=25, x¯(x-bar)=50, and s=7, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

< μ <

Answer 1

solution

= 50

s =7

n = 25

Degrees of freedom = df = n - 1 =25 - 1 = 24

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,24 =2.797 ( using student t table)

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

= 2.797 * (7 / 25) = 3.9

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

- E < < + E

50 - 3.9< <50 + 3.9

46.1 < < 53.9