TOPIC: MATHEMATICS
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Homework Assignment 8
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:
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:
Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes.
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.)
The sample statistic, p = 67/185= 0.3622
The formula for calculating the standard error is
Standard error = √p (1-p) where n is the total sold.
n
=√0.3622(1-0.3622)/185
=0.035338
A 95% confidence interval estimate is 0.3622 ± 2(0.035338)
Giving 0.291524 to 0.432876
With 95% confidence, we estimate that between 0.291 (29.1%) and 0.433 (43.3%) of all treadmills service contracts were sold.
The sample statistic, p = 55/123= 0.44715
The formula for calculating the standard error is
Standard error = √p (1-p) where n is the total sold.
n
=√0.44715 (1-0.44715)/123
=0.04483
A 95% confidence interval estimate is 0.447 ± 1.96 (0.04483).
Giving 0.35913 to 0.53487
Therefore with 95% confidence, we estimate that between 0.359 (35.9%) and 0.535 (53.5%) of exercise bikes were sold.
2.)
There is no major difference between the two. This is because a 95% confidence interval does not give a wider range between two values.
Reference
Eberley College of Science (2015) Constructing confidence intervals to estimate a population proportion Retrieved on 3rd may 2015 from https://onlinecourses.science.psu.edu/stat200/node/48
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