Question

You may need to use the appropriate appendix table or technology to answer this questlon. Studies show that massage therapy has a variety of healh benefits and it is not too expensive. A sample of 14 typical cee-hour massage therapy sessions showed an average charge of $56. The population standard deviation for a ene-hour session is a =$6.5.

(a) What essumptions about the population sheuld we be willing te make if a margin of error is desired? We should be willing to moke the assumption that the population is at least approximately bimodai. We should be willing to make the aswumption that the population is at least approaimately skewed lef. We should be willing to make the assumption that the population is at ieast approximately unitorm. We chould be wiling to make the assumption that the population is at least spproximatedy shewed right. We should be willing to make the assumption that the population is ot least approximately normad,
(b) Using 95% connidence, what is the margin of error in doltars? (Round your answer to the neares cent.)
(c) Using 99% connidence, what is the margin of error in dollars? (Round your answer to the nearest cent.).

Answer 1

To determine the assumptions about the population, we can assume that it is at least approximately normally distributed. The margin of error at 95% confidence is approximately $3.41, while at 99% confidence it is approximately $4.48.

Step-by-step explanation:

(a) To determine the assumptions about the population that can be made for a desired margin of error, we need to consider the shape of the population distribution. In this case, since we do not have any specific information about the shape of the population distribution, we should be willing to make the assumption that the population is at least approximately normally distributed. Therefore, the correct answer is: We should be willing to make the assumption that the population is at least approximately normally distributed.

(b) To calculate the margin of error at a 95% confidence level, we can use the formula:

Margin of Error = Z * (Population Standard Deviation / Square Root of Sample Size)

Plugging in the values, we get:

Margin of Error = 1.96 * (6.5 / Square Root of 14) ≈ 1.96 * 1.739 ≈ 3.41

So, the margin of error is approximately $3.41.

(c) To calculate the margin of error at a 99% confidence level, we can use the same formula:

Margin of Error = Z * (Population Standard Deviation / Square Root of Sample Size)

Plugging in the values, we get:

Margin of Error = 2.58 * (6.5 / Square Root of 14) ≈ 2.58 * 1.739 ≈ 4.48

So, the margin of error is approximately $4.48.