MAT 510 – Homework Assignment
Homework Assignment 6 – Jessica Gibson
Due in Week 9 and worth 30 points
Suppose the number of equipment sales and service contracts that a store sold during the last six (6) months for treadmills and exercise bikes was as follows:
Equipment Sales and Service Contracts Sold
Treadmill
Exercise Bike
Total Sold
185
123
Service Contracts
67
55
The store can only sell a service contract on a new piece of equipment. Of the 185 treadmills sold, 67 included a service contract and 118 did not. Complete the following questions in the space provided below:
1.
Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes. 2.
Is there a major difference between the two pieces of equipment? Why or why not?
Type your answers below and submit this file in Week 9 of the online course shell:
1.
Treadmill service contracts sold = 67
Bike service contracts sold = 55
N1= size of treadmills sample = 185
N2 = size of exercise bikes sample = 123
P1 = sample proportion of treadmill service contracts sold = 67/185 = 0.36216216
P2 = sample proportion of exercise bike service contracts sold = 55/123 = 0.44715447
x1 = population proportion of all treadmill service contracts sold
x2 = population proportion of all exercise bike service contracts sold
36 − .45 √ .4 ( 1 − .4 )( 1 185 + 1 123 ) = − .09 √ ( .4 ) ( .6 ) ( .005 + . 008 ) = − .09 .06 = - 1.50
2.
Yes, there is a major difference between the treadmill and exercise bikes. The reason being is because there were more treadmill contracts sold then the exercise bikes. There are differences in the percentages of equipment sold with service contracts. The difference is approx. -0.197 to 0.027. Being that there were more treadmill contracts that doesn’t seem to change anything because the percentages are so close together telling me that there is probably not a major proportional difference.
