Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

n = 30,  = 84.2, s = 18.4, 90% confidence

Answer 1

b )Given that,

= 84.2

s =18.4

n = 30

Degrees of freedom = df = n - 1 =30 - 1 = 29

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,29 =1.699    ( using student t table)

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

= 1.699 * (18.4 / 30) = 5.7

The 90% confidence interval is,

- E < < + E

18.4 -5.7 < < 18.4+ 5.7

12.7 < < 24.1

( )