Question

Studies show that massage therapy has a variety of health benefits. A sample of 46 typical one-hour massage therapy sessions showed an average charge of $70. The population standard deviation for a one-hour session is $5.63. Estimate with 92% confidence the average charge of all one-hour massage therapy sessions. (Round to 2 decimal places.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $70

Population standard deviation =    = $5.63

Sample size = n =46

At 92% confidence level the z is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 = 0.08/ 2 = 0.04

Z_/2 = Z_0.04 = 1.75

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

= 1.75 * (5.63 /  46 )

= 1.45
At 95% confidence interval estimate of the population mean
is,

- E < < + E

70 -1.45 <   <70 + 1.45


( ,68.55 ,71.45)