Question

If n=11, ¯xx¯(x-bar)=43, and s=4, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

Answer 1

Solution :

Given that,

= 43

s = 4

n = 11

Degrees of freedom = df = n - 1 = 11 - 1 = 10

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,10 =2.228

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

= 2.228 * (4 / 11) = 2.7

The 95% confidence interval estimate of the population mean is,

- E < < + E

43 - 2.7< < 43 + 2.7

40.3 < < 45.7

(40.3, 45.7)