College Statistics problem help

Question

A weight loss center provided a loss for 72% of its participants.  The center’s leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.  Test an appropriate hypothesis to see if the new method leads to an improvement in the clients’ success rates. 
 

Generate a null and alternate hypothesis (.72):
 
 
 
 What is the z test statistic?
 

 What is the p-value?

 
Do you REJECT or RETAIN the null hypothesis at the 1% level? 

Answer 1

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.