Assuming the population has a bell-shaped distribution

Question

Assuming the population has a bell-shaped distribution, if a sample size n=9 has a sample mean x¯=45 with a sample standard deviation s=10, find the margin of error (MOE) at a 90% confidence level. Round the answer to two decimal places.



Answer 1

sample mean = xbar = 45

sample standard deviation = s = 10

sample size = 9

alpha = 1-.90 = .10 for 2 tails

assume normal distribution

use z tables or a z calculator, if n is large

z=1.645 for 90% CI

but 9 is too small

use t tables or a t calculator

t = 1.860 for def = 9-1=8, not that far from 1.645 though

to find critical value = 1.860

CI = xbar +/-ts/sqrn

=45 +/-(1.86)(10)/3

= 45+/-6.2

= (38.8, 51.2) with 90% Confidence for n=9, s=10, xbar=45

MOE = 6.20