SOLUTION: A health club manager claims that its members lose an average of 13 pounds during the first six months of membership. A sample of 15 members of this health club showed that they lo

Question 1035362: A health club manager claims that its members lose an average of 13 pounds during the first six months of membership. A sample of 15 members of this health club showed that they lost on average 11.5 pounds during the first six months of membership with a standard deviation of 2.15 pounds. Test at the 2.5% significance level if the mean weight lost during the first six month of their membership by all members of the health club is less than 13 pounds.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A health club manager claims that its members lose an average of 13 pounds during the first six months of membership. A sample of 15 members of this health club showed that they lost on average 11.5 pounds during the first six months of membership with a standard deviation of 2.15 pounds. Test at the 2.5% significance level if the mean weight lost during the first six month of their membership by all members of the health club is less than 13 pounds.
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Ho: u >= 13 (claim)
Ha: u < 13 (the question)
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x-bar = 11.5
t(11.5) = (11.5-13)/[2.15/sqrt(15)] = -2.70
p-value = P(t < -2.70 when df = 14) = tcdf(-100,-2.7,14) = 0.008
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Conclusion:: Since the p-value is less then 2.5%, reject Ho.
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The test results support the conclusion that less than 13 lbs
were lost by all members of the club.
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Cheers,
Stan H.
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