Question

Studies show that massage therapy has a variety of health benefits and it is not too expensive. A sample of 11 typical one-hour massage therapy sessions showed an average charge of $58. The population standard deviation for a one-hour session is $4.95.

a. What assumptions about the population should we be willing to make if a margin of error is desired?

b. Using 90% confidence, what is the margin of error (to 2 decimals)?

c. Using 95% confidence, what is the margin of error (to 2 decimals)?

Answer 1

a)
The data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ).
The data must be reasonably random.

b)
sample standard deviation, σ = 4.95
sample size, n = 11

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

ME = zc * σ/sqrt(n)
ME = 1.64 * 4.95/sqrt(11)
ME = 2.45

c)
Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 4.95/sqrt(11)
ME = 2.93