Question 188882: Suppose the Real Estate Board of Greater Vancouver conducts a study of the number of first-time applicants who are successful in passing the certification examination for real estate salespeople on their first attempt. Two samples were taken from the list of applicants: those who were already employed by a real estate agency and those who were recent university graduates who had not taken a full-time job. Results are shown in the table below:
Real Estate Employees Unemployed Graduates
Sample Size 100 200
Number passing 47 102
a.What is the sample proportion of real estate employees who passed the exam on their first attempt?
b.What is the sample proportion of unemployed college graduates who passed the exam on their first attempt?
c.If the null hypothesis is H0: R – U = 0, what is the value of the test statistic? R = proportion of real estate employees passing the exam on their first attempt, U = proportion of unemployed graduates passing the exam on their first attempt.
d. State your conclusion on the result of the test for H0: R – U = 0 if the alternate hypothesis is: H0: R – U < 0. Use = 0.05.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! -----------------
Suppose the Real Estate Board of Greater Vancouver conducts a study of the number of first-time applicants who are successful in passing the certification examination for real estate salespeople on their first attempt.
Two samples were taken from the list of applicants: those who were already employed by a real estate agency and those who were recent university graduates who had not taken a full-time job.
Results are shown in the table below:
Real Estate Employees Unemployed Graduates
Sample Size 100 200
Number passing 47 102
a.What is the sample proportion of real estate employees who passed the exam on their first attempt?
47/100 = 0.47
---------------------
b.What is the sample proportion of unemployed college graduates who passed the exam on their first attempt?
102/200 = 0.51
---------------------
c.If the null hypothesis is Ho: pR – pU = 0, what is the value of the test statistic? pR = proportion of real estate employees passing the exam on their first attempt, U = proportion of unemployed graduates passing the exam on their first attempt.
-------
z(0.47-0.51) = -0.04/sqrt[(.5*.5/100) + (.5*.5/200)] = -0.6532
p-value = P(-100 < z < -0.6532) = 0.2568
----------------------------------------------------------
d. State your conclusion on the result of the test for H0: R – U = 0 if the alternate hypothesis is: H0: R – U < 0. Use = 0.05.
---
Since the p-value is greater than 5%, fail to reject Ho.
The population proportions of the two groups are statistically the same.
====================================
If there are parts of this you do not understand you should ask
for clarification.
====================================
Cheers,
Stan H.
|
|
|
