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 $61. The population standard deviation for a one-hour session is = $5.3 .

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

- Select your answer -The population has uniform distribution, The population is at least approximately normal is required, The population has exponential distribution, No assumptions should be made

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

c. Using 99% confidence, what is the margin of error (to 2 decimals)?

Answer 1

Solution :

Given that,

= $61

= $5.3

n = 11

a) The population is at least approximately normal is required.

b) At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * ( 5.3 / 11)

Margin of error = 3.13

c)

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (5.3 / 11)

Margin of error = 4.12