Question

If n = 19, ¯ x = 43, and s = 17, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

< μ

Answer 1

Solution :

Given that,

=43

s = 17

n = 19

Degrees of freedom = df = n - 1 = 19- 1 = 18

a ) At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2 = 0.20/ 2 = 0.10

t _/2,df = t_0.10,18 =1.330

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

= 1.330 * (17 /  19) = 5.187

The 80% confidence interval estimate of the population mean is,

- E < < + E

43 - 5.187 < < 43+ 5.187

37.813 < < 48.187