Question

Studies show that massage therapy has a variety of health benefits and it is not too expensive.† A sample of 13 typical one-hour massage therapy sessions showed an average charge of $56. The population standard deviation for a one-hour session is σ = $7.5. (a) What assumptions about the population should we be willing to make if a margin of error is desired? We should be willing to make the assumption that the population is at least approximately normal. We should be willing to make the assumption that the population is at least approximately skewed right. We should be willing to make the assumption that the population is at least approximately skewed left. We should be willing to make the assumption that the population is at least approximately bimodal. We should be willing to make the assumption that the population is at least approximately uniform. (b) Using 95% confidence, what is the margin of error in dollars? (Round your answer to the nearest cent.) $ (c) Using 99% confidence, what is the margin of error in dollars? (Round your answer to the nearest cent.)

Answer 1

Answer : we have given :

sample size = n = 13

μ = popualation mean = 56 and

σ = population standard deviation = 7.5

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

Answer :

We should be willing to make the assumption that the population is at least approximately normal.

( because the sample size is small and thus we cannot use central limit therom to obtain that the sampling distribution approximately normal )

(b) Using 95% confidence, what is the margin of error in dollars?  

ME = margin of error = critical value * σ / SQRT(n)

critical value for α = 95 % =  ± 1.96 ( from statistical table for z test )

and  σ / SQRT(n) = 2.0801

ME = (1.96 *  2.0801)

= 4.08   in dollars  (Round your answer to the nearest cent )

(c) Using 99% confidence, what is the margin of error in dollars?

ME = margin of error = critical value * σ / SQRT(n)

critical value for α = 99 % =  ± 2.58 ( from statistical table for z test )

and  σ / SQRT(n) = 2.0801

ME = (2.58 *  2.0801)

= 5.37   in dollars (Round your answer to the nearest cent )