Question

Compute E, the margin of error for the t interval, for a 90% confidence interval for m if a random sample of size n = 40 with sample standard deviation s = 2.8 is drawn from a population with s unknown.

Answer 1

)Given that,

s =2.8

n = 40

Degrees of freedom = df = n - 1 =40 - 1 = 39

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,90 = 1.685 ( using student t table)

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

=1.685 * (2.8 / 40) = 0.746