Question

Studies show that massage therapy has a variety of health benefits. A sample of 48 typical one-hour massage therapy sessions showed an average charge of $72. The population standard deviation for a one-hour session is $5.46. Estimate with 94% 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 94% confident that the charge of one-hour massage therapy sessions is between and dollars.

We are 94% confident that the population mean a charge of all one-hour massage therapy sessions is between (blank) and (blank) dollars.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 72

Population standard deviation = = 5.46

Sample size = n = 48

Z_/2 = 1.88

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

= 1.88 * (5.46 / 48)

= 1.48

At 94% confidence interval estimate of the population mean is,

- E < < + E

72 - 1.48 < < 72 + 1.48

70.52 < < 73.48

(70.52 , 73.48)

We are 94% confident that the charge of one-hour massage therapy sessions is between 70.52 and 73.48 dollars.

We are 94% confident that the population mean a charge of all one-hour massage therapy sessions

is between 70.52 and 73.48 dollars .