A restaurant chain negotiated a new contract with a popular food delivery platform. Starting next year, the platform will charge higher commissions to restaurants for orders that keep a delivery driver waiting.

As an owner of 20 franchises,  would like to better understand whether your restaurants are able to prepare the orders received from the delivery platform, before or shortly after the drivers arrive. I collected data on the most recent 16 orders from each restaurant, and recorded in the Excel sheet Q2.xlsx the time elapsed (in minutes) between receiving each order and when each order is ready to be picked-up.

(a) To understand whether some of your restaurants are faster or slower than the others, you generate the X-bar control chart for the preparation times. Is the process in control? Is there any restaurant that is significantly slower than the others?

(b) What would you do to figure out if some of your restaurants are in fact consistently faster than the others?

  

Order 1 Order 2 Order 3 Order 4 Order 5 Order 6 Order 7 Order 8 Order 9 Order 10 Order 11 Order 12 Order 13 Order 14 Order 15 Order 16 Restaurant 1 4.18 1.24 1.57 4.09 3.09 6.03 7.78 4.71 7.75 8.51 7.15 6.44 4.64 2.69 6.35 6.18 3.17 3.66 5.76 3.26 5.25 7.12 6.52 2.47 8.66 5.01 3.49 Restaurant 2 9.09 Restaurant 3 11.07 Restaurant 4 7.73 4.34 5.65 8.44 4.94 6.34 5.94 7.1 4.33 7.2 7.53 8.03 9.7 6.17 6.3 Restaurant 5 2.81 7.44 5.64 4.2 3.2 2.11 4.04 5.58 7.33 Restaurant 6 1.88 2.23 1.53 5.07 5.56 6.84 6.3 6.8 1.93 5.01 10.04 2.49 3.01 6.29 2.37 3.65 6.95 6.48 6.23 8.89 6.65 8.94 7.02 10.84 5.04 4.34 8.14 4.26 1.27 1.06 2.49 2.6 2.55 2.14 3.77 3.55 7.08 7.65 6.2 4.71 6.45 3.71 7.38 7.68 2.97 5.01 4.94 2.49 8.83 6.29 Restaurant 7 5.73 7.07 5.22 2.53 Restaurant 8 5.77 5.01 3.36 5.14 5.78 3.39 9.19 8.49 8.97 3.06 2.87 Restaurant 9 1.2 3.58 1.59 7.75 Restaurant 10 1.68 3.81 6.92 5.78 6.22 Restaurant 11 5.79 5.38 2.33 3.93 5.52 8.13 8.28 7.05 7.32 9.57 1.49 8.58 4.71 5.07 5.71 8.33 6.46 7.72 3.59 3.11 4.71 4.02 6.05 5.55 5.71 2.35 5.62 3.7 4.84 5.71 7.44 2.88 3.9 4.23 7.93 1.99 5.79 7.1 6.21 1.63 3.27 4.66 3.75 1.54 6.21 5.67 4.2 4.17 6.95 10.17 4.58 7.34 3.67 3.2 6.61 5.01 10.69 4.27 4.56 2.55 9.96 12.53 Restaurant 12 Restaurant 13 8.03 7.36 3.07 Restaurant 14 2.95 4.96 7.4 Restaurant 15 12.54 12.9 18.98 Restaurant 16 6.37 10.37 Restaurant 17 4.93 8.13 Restaurant 18 2.65 2.03 Restaurant 19 2.53 5.41 Restaurant 20 5.17 6.54 5.8 2.75 3.72 4.93 4.84 2.26 7.92 11.02 7.63 5.92 8.17 1.63 5.82 5.34 4.88 4.21 5.68 6.73 6.66 7.38 4.42 4.15 7.29 5.2 7.81 7.8 2.18 6.37 3.81 2.29 1.13. 1.88 5.93 5.83 3.54 5.95 7.72 6.08 1.63 2.62 7.37 4.56 5.58 6.24 2.72 5.43 4.03 10.24 1.7 1.23 8.38 13.22 3.11 4.24 3.88 1.82 2.01 3.83 3.65 5.98 4.08 2.05 6.16 3.76 1.26 3.4 5.96 4.51 3.43 4.5 5.88 3.37 3.14 2.44 2.2 4.16 1.86 5.03 5.63 3 9.37 4.49 10.73 4.68 6.1 4.42 5.32 7.04 5.51 8.18 10.16 10.29 5.13 6.9 3.25 5.57 4.27 5.3 2.75 5.27 5.45 8.52 6.2 5.07 2 1.71 9.61 3.43 4.46 3.06 5.41 5.51