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 = 12,  = 23.6, s = 6.6, 99% confidence

Answer 1

solution

Given that,

= 23.6

s =6.6

n = 12

Degrees of freedom = df = n - 1 =12 - 1 = 11

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,11 = 3.106 ( using student t table)

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

= 3.106 * ( 6.6/ 12) = 5.92

The 99% confidence interval is,

- E < < + E

23.6 - 5.92  < < 23.6 +  5.92

17.68 < < 29.52