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. 
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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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