Question

The business manager of a local health clinic is interested in estimating the difference between the fees for extended office visits in her center and the fees of a newly opened group practice. She gathered the following information regarding the two offices.

	Health Clinic		Group Practice
Sample size	50 visits		45 visits
Sample mean	$21	$19
Sample Standard deviation	$2.75	$3.00

a. Determine the degrees of freedom for the t-distribution.

b. Use the p-value approach and test to determine if the average fee of the health clinic is significantly higher than that of the group practice.

c. Sate the null and alternative hypothesis.

d. What is your conclusion?

Answer 1

Solution: Here the given information are

Health Clinic

sample size n1=50 , sample mean==21, sample standard deviation=s1=2.75

Group Practice

sample size=45, sample mean==19 , sample standard deviation=s2=3

a) Degress of freedom of the distribution

degrees of freedom = n1+n2-2= 50+45-2=93

b) Test statistic:

Sp=2.8710

t*=

t*=3.39

P-value=0.00051 --------------( from excel tdist(x,df,tails)

From the P-value we reject H0.

c) Null hypothesis:H0:

Alternative hypothesis:H1:

d) We can conclude that the average fee of the health clinic is significantly higher than that of the group practice.