Question

Studies show that message therapy has a variety of health benefits a sample of 11 typical one-hour massage therapy sessions showed an average charge of $57 the population standard deviation for one-hour session is $5.25

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

b) using 90% confidence , what is the margin of error?

c) Using 95% confidence, what is the margin of error?

Answer 1

a)

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

b)

Mean = 57

Sample size (n) = 11

Standard deviation (s) = 5.25

Confidence interval(in %) = 90

t = 2.2281

Required confidence interval = (57.0-3.5269, 57.0+3.5269)

Required confidence interval = (53.47, 60.53)

c)

Mean (\bar{x}) = 57

Sample size (n) = 11

Standard deviation (s) = 5.25

Confidence interval(in %) = 95

t = 2.490

Required confidence interval = (57.0-3.9415, 57.0+3.9415)

Required confidence interval = (53.06, 60.94)

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