Question

If n = 13, ¯xx¯ = 48, and s = 20, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

answer ____ < μμ < ____ answer

Looking for two answer before and after.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 48

sample standard deviation = s = 20

sample size = n = 13

Degrees of freedom = df = n - 1 = 12

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,12 = 3.055

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

= 3.055 * (20 / 13)

= 16.946

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

- E < < + E

48 - 16.946 < < 48 + 16.946

31.054 < < 64.946