Neighborhood retailers often advertise using flyers. People deliver the flyers to homes and are paid according to the number of flyers delivered. Recently, a new company has developed a service which it claims is better than the old company. A retailer wanted to know whether the delivery rate of the new company was better than the delivery rate of the existing company. Random samples of homes were drawn, and homeowners were asked if they had received the flyer (1 = no, 2 = yes). Assume a = 0.10. Use the Excel tables (use the correct one!) below to answer the following questions:
z-Test: Two Proportions
Sample Proportions 0.948 (new) 0.92 (older)
Observations 250 (new) 250 (older)
Hyothesized Difference 0
z-statistic: 1.26
P(Z<=z) One-Tail 0.1037
z Critical One-Tail 1.2816
P(Z<=z) Two-Tail 0.2074
z Critical Two-Tail 1.6449
z-Estimate: Two Proportions
Sample Proportions 0.948 (new) 0.92 (older)
Observations 250 (new) 250 (older)
LCL -0.0085
UCL 0.0645
1) In testing the difference of proportions (is the proportion of flyers delivered by the new company higher than the proportions delivered by the existing company), what is the test statistic? (Use the exact figure from the table provided.)
2) What is the critical value to use in this hypothesis test? (Use the exact figure in the table.)
3) What is the p-value? (Use the exact figure in the table.)
4) Estimate the difference between the two proportions using a 90% confidence level (same assumption was used for the tables). The lower confidence limit is ___
5) Estimate the difference between the two proportions using a 90% confidence level (same assumption was used for the tables). The upper confidence limit is ___
6) Based on this analysis, the retailer would conclude that the new company has a higher delivery rate than the existing company. (True or False?)