question archive Studies show that message therapy has a variety of health benefits a sample of 10 typical one-hour massage therapy sessions showed an average charge of $59 the population standard deviation for one-hour session is $5
Studies show that message therapy has a variety of health benefits a sample of 10 typical one-hour massage therapy sessions showed an average charge of $59 the population standard deviation for one-hour session is $5
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Studies show that message therapy has a variety of health benefits a sample of 10 typical one-hour massage therapy sessions showed an average charge of $59 the population standard deviation for one-hour session is $5.50 a) what assumptions about the population should we be willing to make if a margin of error is desired b) using 95% confidence , what is the margin of error? c) Using 99% confidence, what is the margin of error?
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Answer:
sample size,n = 10
sample mean,x = 59
standard deviation,s = 5.5
a.
Since sample size is less than 30 then it is assumed that the population is normally distributed.
b.
Since population standard deviation is given use z-statistic
alpha,a = 1-0.95 = 0.05
Za/2 = Z0.025 = 1.96
margin of error:
Za/2 * (s/sqrt(n))
= 3.4089
c.
alpha,a = 1-0.99 = 0.01
Za/2 = Z0.005 = 2.575
margin of error:
Za/2 * (s/sqrt(n))
= 4.4786
