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

    • Posted: 22 days ago
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