# MAT 510 WEEK 9 QUIZ

Description

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 195 138

Service contracts 60 45

The store can only sell a service contract on a new piece of equipment. Of the 195 treadmills sold, 60 purchased a service contract. Of the 138 exercise bikes, 45 purchased a service contract.

Remember to watch the instructional video and use the excel template provided to help you with the math.

Complete the following questions in the space provided below:

- Is there a major difference between the two pieces of equipment? Why or why not?
- Interpret the meaning of the confidence interval for Treadmills at a 95% confidence level.
- Interpret the meaning of the confidence interval for Exercise Bikes at a 95% confidence level.
- Are confidence intervals one-tailed or two-tailed?
- Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes.

**Question 1 **

Are confidence intervals one-tailed or two-tailed?

TWO-TAILED

ONE-TAILED

2 points

**Question 2 **

- Interpret the meaning of the confidence interval for Treadmills at a 95% confidence level.

95% of people purchased between 24 and 37 contracts after buying treadmills.

We are 95% confident that the number of contracts purchased is between 24.3 and 37.2

We are 95% confident that customers who purchased contract after purchasing treadmills is approximately between 24% and 37%.

Unable to determine this value given the information provided.

4 points

**Question 3 **

- Interpret the meaning of the confidence interval for Exercise Bikes at a 95% confidence level.

We are 95% confident that the percentage of customers that purchased Exercise Bikes is between 25% and 40%.

We are 95% confident that the percentage of customers that purchased Exercise Bikes is between 25 and 40 contracts.

We are 95% confident that the percentage of customers that purchased Exercise Bikes is more than 50%

Unable to determine this information.

4 points

**Question 4 **

- Using the two-proportion confidence interval formula we determine if there is a difference between the two proportions. Is there a difference between the proportions?

Yes

There is no difference because the confidence interval contains zero since the interval is between (-12% and 8%)

Unable to determine this information given insufficient evidence.

Yes. The because we are 95% confident that the percentage of customers who -purchase contracts is under 12% and 8%

10 points

**Question 5 **

- Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes. You may want to use this site to check your calculations: http://vassarstats.net/prop2_ind.html

(-12, 8)

(8,12)

(-12%, 8%)

Unable to determine

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