Question

If n = 17, ¯ x = 42, and s = 20, construct a confidence interval at a 90% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

? < μμ < ?

Answer 1

Given that,

= 42

s =20

n = 17

Degrees of freedom = df = n - 1 =17 - 1 =16

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,16 =1.746 ( using student t table)

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

= 1.746 * (20 / 17) = 8.469

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

- E < < + E

42 -8.469 < < 42+ 8.469

33.531 < < 50.469