document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #650028 by stanbon(75887)\"\" \"About 
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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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\n" ); document.write( "Ho: u >= 13 (claim)
\n" ); document.write( "Ha: u < 13 (the question)
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\n" ); document.write( "x-bar = 11.5
\n" ); document.write( "t(11.5) = (11.5-13)/[2.15/sqrt(15)] = -2.70
\n" ); document.write( "p-value = P(t < -2.70 when df = 14) = tcdf(-100,-2.7,14) = 0.008
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\n" ); document.write( "Conclusion:: Since the p-value is less then 2.5%, reject Ho.
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\n" ); document.write( "The test results support the conclusion that less than 13 lbs
\n" ); document.write( "were lost by all members of the club.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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