Question

Studies show that massage therapy has a variety of health benefits. A sample of 41 typical one-hour massage therapy sessions showed an average charge of $65. The population standard deviation for a one-hour session is $5.54. Estimate with 97% confidence the average charge of all one-hour massage therapy sessions.  (Round to 2 decimal places.)

Complete the following sentence to provide an interpretation of the confidence interval in the context of the problem:

We are 97% confident that the  (Click to select)samplepopulation   (Click to select)meanstandard deviation  charge of  (Click to select)all41 one-hour massage therapy sessions is between    and  dollars.

Answer 1

97% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

65 - 2.1701 * 5.54 / sqrt(41) < < 65 + 2.1701 * 5.54 / sqrt(41)

63.12 < < 66.88

95% CI is ( 63.12 , 66.88 )

Interpretation -

We are 97% confident that the population mean charge of all 41 one hour massage therapy sessions

is between 63.12 and 66.88 dollars.