Question

A random sample of 14 size AA batteries for toys yield a mean of 3.23 hours with standard deviation, 0.54 hours. (a) Find the critical value, t*, for a 99% CI (give to at least 3 decimal places). t* =

(b) Find the margin of error for a 99% CI (give to at least 2 decimal places).

Answer 1

solution

Given that,

= 3.23

s =0.54

n = 14

Degrees of freedom = df = n - 1 =14 - 1 = 13

(a)

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

critical value = t /2,df = t0.05,13 =1.771 ( using student t table)

(b)

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

= 1.771* ( 0.54 / 14) = 0.26