Answer to Question #307058 in Statistics and Probability for tahmid

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.