Math 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:

1. Is        there a major difference between the two pieces of equipment? Why or why        not?
2. Interpret        the meaning of the confidence interval for Treadmills at a        95% confidence level.
3. Interpret        the meaning of the confidence interval for Exercise Bikes at a        95% confidence level.
4. Are        confidence intervals one-tailed or two-tailed?
5. 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 

1. 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 

1. 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 

1. 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 

1. 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