Question

Studies show that massage therapy has a variety of health benefits and it is not too expensive. A sample of 10 typical one-hour massage therapy sessions showed an average charge of $59. The population standard deviation for a one-hour session is σ = $5.50. Develop a 95% confidence interval for the mean cost of massage therapy sessions.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 59

Population standard deviation =    = 5.50

Sample size n =10

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   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 5.50/ 10 )

= 3.4
At 95% confidence interval mean
is,

- E < < + E

59-3.4 , 59+3.4

(55.6 , 62.4)