Question

You may need to use the appropriate appendix table or technology to answer this question.

Studies show that massage therapy has a variety of health benefits and it is not too expensive. A sample of 11 typical one-hour massage therapy sessions showed an average charge of $51. 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 uniform.     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 bimodal.We should be willing to make the assumption that the population is at least approximately skewed left.

(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

Given,

sample size = n = 11

μ = popualation mean = 51 and

σ = population standard deviation = $7.5

a) 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)  

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) = 2.2613

ME = (1.96 * 2.2613)

= $4.43

c)

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) = 2.2613

ME = (2.58 *  2.2613)

= $5.83