Message therapy Probability

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 57 dollars. The population standard deviation for a one-hour session is o=$5.15

a. What assumptions about the population should we be willing to make if a margin of error is desired?

- Select your answer -The population has uniform distribution or The population is at least approximately normal is required or The population has exponentional distribution or No assumptions should be made

b. Using 90% confidence, what is the margin of error (to 2 decimals)?

c. Using 99% confidence, what is the margin of error (to 2 decimals)?

Answer 1

Part I, assumptions about the random variables must be made. Before we can use inferential statistics we HAVE to know, or be relatively sure of the distribution of the variable involved. Based on the normal sources of variation in simple prices a normal or approximately normal distribution would be appropriate to assume. The other assumptions are just not supported.

Part II, as the σ (population standard deviation) is known, and a sample size is not given (i.e. population parameters only) the MOE formula for the range of charges would use the Z distribution and standard deviation

MOE = Z_α/2 * σ For 90% confidence the Z_α/2 = 1.645 and the MOE would be $8.47

Part III, this is the same as Part II using the 99% confidence value of the Z_α/2 times sigma or 2.576

MOE would be 2.576 *5.15 or $13.27