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 and Service Contract Sales |
||
|
Treadmill |
Exercise Bike |
|
|
Equipment Sales |
185 |
123 |
|
Service Contract Sales |
67 |
55 |
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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.
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Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes.
P1= proportion of trend mills
67/185= 0.3622
P2= proportion of exercise bikes
55/123= 0.4472
Group 1
No. of items of interest = 67
Sample size =185
Proportion =0.3622
Group 2
No. of items of interest =55
Sample size =123
Proportion = 0.4472
Difference in the proportion (p1-p2) = -0.0850
CA for p1-p2 is C1 = P1-P2 +/- Z x se
Where se= √(P1X(1-P1)/N1+P2(1-P2)/N2)
Se=0.0571
Value for 95% confidence level =1.96
95% C1 = -0.0850 +/- 1.96x0.0571
(-0.1969 , 0.02689)
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Determine if there is or not a major difference between the two pieces of equipment? Why or why not?
There is no major difference between the two pieces of equipment since the 95% confidence interval between the proportions of service contracts sold on treadmills versus exercise bikes contains 0 values.
An analysis on the proportions of service contracts sold on treadmills versus exercise bikes it is evident that the exercise bikes sold a higher percentage of equipment including a service contracts. A look at the equipment sold percentages with service contract, the treadmills sold 36.2162% of their total inventory and the exercise bikes sold 44.7154% of their total inventory ( Peck, Olsen & Devore, 2015) .
Reference
Peck, R., Olsen, C., & Devore, J. L. (2015). Introduction to statistics and data analysis . Cengage Learning.
