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