Stephan Kpoti G. answered • 08/13/15

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Let

P be the proportion of participant who lost weight with the new method.

Po be the mean weight loss normally provided by the center (Po=72%)

Pm be the mean weight loss of the sample group (Pm=78%)

N be the sample size

Hypothesis

Ho: the proportion of participants who lost weight with the new method is 72%; P=0.72

Ha: the proportion of participants who lost weight with the new method is greater than 72%; P>072

Compute the z-statistic

z=(Pm-Po)/√(Po(1-Po)/N)=(0.78-0.72)/√(0.72(1-0.72)/140)=1.58

Find the P-value

p-value= P(z>1.58)=1-P(z<1.58)=1-0.9429=0.0571

Conclusion:

p-value=0.0571>0.01, Do not reject Ho

At 1% significance level, the data do not provide enough evidence to conclude that the new method provide a loss for more than 72% of participants.