Delivery Times at Snow Pea Restaurant

The SnowPea Restaurant is a Chinese carryout/delivery restaurant. Most of SnowPea’s deliveries are within a 10-mile radius, but it occasionally delivers to customers more than 10 miles away. SnowPea employs a number of delivery people, four of whom are relatively new hires. The restaurant has recently been receiving customer complaints about excessively long delivery times. Therefore, SnowPea has collected data on a random sample of deliveries by its four new delivery people during the peak dinner time. The data are in the file SNOWPEA.XLS.

The variables are:

Develop a report that makes reasonable recommendations to SnowPea management. SnowPea is concerned that one or more of the new delivery people might be slower than others.

1. Begin by estimating the mean delivery time for each delivery person to 95% accuracy.
2. Although these might be interesting, give reasons why they are not really fair measures for comparing the efficiency of the delivery people.
3. Estimate the mean speed of delivery for each delivery person, where speed is measured as miles per hour during the trip from SnowPea to the customer.
4. Compare the two sets of intervals you have constructed. Are there any other differences (by deliverer) that are apparent?
5. Perform the necessary hypothesis tests to investigate.
   SnowPea would like to advertise that it can achieve a total delivery time of no more than M minutes for all customers within a 10-mile radius. On all orders that take more than M minutes, SnowPea will give the customers a $10 certificate on their next purchase.
6. Does this seem like a reasonable idea?
   Yes, we would perform a one-sided null hypothesis test using M as the null and anything more than as the alternative hypothesis. If the answer is more than M or in its range given a 95% confidence level we would not recommend giving customers a $10 certificate on their next purchase.
7. Investigate a few different values for M, and determine the proportion of deliveries (overall) that conform, and then break it up by delivery person, to see if there are any differences.
   We looked at 20, 30, & 40 minute delivery times. Twenty was too close to our mode of 17.8. Forty was too high because the upper lower values were out of the range. We decided on 30 because the range was most representative of our sample.
   Null Hypothesis: If a delivery is more than 30 minutes in time the customer will receive a $10 gift certificate. Given M = 30 minutes than we would have to reject this hypothesis since the range is (lower) 28.4 and (upper) 31.6 and the sample mean is 16.7.
   Overall, the proportion of deliveries that conform is: the mean of our sample is 16.74 minutes which is below our range’s lower value.
   Delivery Person 1: 12.25 (20) 61% (30) 41% (40) 31%
   Delivery Person 2: 14.73 (20) 74% (30) 49% (40) 37%
   Delivery Person 3: 19.72 (20) 99% (30) 66% (40) 49%
   Delivery Person 4: 20.24 (20) 1.01% (30) 67% (40) 51%
8. & (9) Are there significant differences in proportion for the different values of M you have chosen?

Yes, because the twenty minute delivery time gives you too close of a percentage to our mode. Forty minute delivery time is too high for our range.

(10) Assuming for now that the delivery people in the sample are representative of all of SnowPea’s delivery people, estimate (to 90% certainty) the proportion of deliveries (within the 10- mile limit) that will be on time for your different values of M.

Twenty minutes, 71% of the drivers would be within the twenty minute timeframe.

Thirty minutes, 47% of the drivers would be within the thirty minute timeframe.

Forty minutes, 35% of the drivers would be within the forty minute timeframe.

(11) Suppose SnowPea makes 1000 deliveries within the 10-mile limit. For each of your values of M in part a, develop 90% confidence intervals for the total dollar amount of certificates it will have to give out for being late.

(11b) which value of M do you recommend?

M = 30 & 29.7 – 30.34

(12) Determine the probability (for each driver) of being late given each value of M you investigated.

(13) Using this probability, determine the total dollar amount of certificates it will have to give out for being late if each driver makes 1000 deliveries.

(14) Using decision analysis, should any action be taken for any of the drivers?

(15) What are your conclusions regarding each of the drivers.

(16) Summarize your recommendations to Snow Pea in a report.

Price: $12.93

Solution: The downloadable solution consists of 4 pages, 893 words.
Deliverable: Word Document