Discuss the below:
Q1. SafeRoad Stores is redesigning the checkout lanes in its stores throughout the country. Two designs have been suggested. Tests on customer checkout times have been conducted at two stores where the two new systems have been installed. A summary of the sample data follows:
System A System B
Sample size = 25 Sample size = 25
Sample mean checking out time = 4.3 minutes Sample mean checkout time = 3.3 minutes
Sample standard deviation = 2.0 minutes Sample standard deviation = 3.0 minutes
At the 0.05 significance level, perform a statistical test to see the two systems are significantly different.
Q2. 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
Number passing 100
47 200
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: πR - πU = 0, what is the value of the test statistic? πR = proportion of real estate employees passing the exam on their first attempt, πU = proportion of unemployed graduates passing the exam on their first attempt.
d. State your conclusion on the result of the test for H0:πR - πU = 0 if the alternate hypothesis is: H0: πR - πU < 0. Use α = 0.05.