Question

Problem 1- Confidence Interval Studies show that massage therapy has a variety of health benefits and it is not too expensive (Wall Street Journal, March 13, 2012). A sample of 10 typical one-hour massage therapy session showed an average charge of $59. The population standard deviation for a one hour session is ơ $5.5 What assumptions about the population should we be willing to make if the margin of error is desired? Using 95% confidence, what is the margin of error? what is the 95% confidence interval of the population mean? Interpret this interval. Please refer to the following table to get the z value a. b. Confidence level 90% 95% /2 10 05 05 025 1.645 1.960

Answer 1

sample size, n =10

sample mean, x =59

standard deviation ,s = 5.5

a).

since sample size is less than 30 then it is assumed that the population is normally is distributed.

b).

since population standard deviation is given use z-statistics

alpha,a= 1-0.95 =0.05

Za/2 =Z0.025 =1.96

margin of error :

Za/2* (s/sqrt(n))

= 3.4089

c).Here i am using 99% confidence interval and margin of error

alpha,a =1- 0.99 =0.01

Za/2 =Z0.005 =2.575

margin of error :

Za/2 *(s/sqrt(n))

=4.4786