Question

The management of Priority Health Club claims that its members lose

an average of 10 pounds or more within the first month after joining

the club. A consumer agency that wanted to check this claim took a

random sample of 36 members of this health club and

found that they

lost an average of 9.2 pounds within the first month of membership

with a population standard deviation of 2.4 pounds. Find the

p

–

value

for this test. What will you decision be if

α

=

.01?

Answer 1

$H_0: \mu=10.$

$H_a:\mu>10.$

Test statistic: $z=\frac{9.2-10}{\frac{2.4}{\sqrt{36}}}=-2.$

P-value: $p=P(Z>-2)=0.9772.$

Since the p-value is greater than 0.01, fail to reject the null hypothesis.