The time needed for checking in at a motel is to be investigated. Historically, the process has had a standard deviation equal to .146. The means of 39 samples of n = 14 are shown in the following table.

Sample Mean Sample Mean Sample Mean Sample Mean 1 3.86 11 3.88 21 3.84 31 3.88 2 3.90 12 3.86 22 3.82 32 3.76 3 3.83 13 3.88 23 3.89 33 3.83 4 3.81 14 3.81 24 3.86 34 3.77 5 3.84 15 3.83 25 3.88 35 3.86 6 3.83 16 3.86 26 3.90 36 3.80 7 3.87 17 3.82 27 3.81 37 3.84 8 3.88 18 3.86 28 3.86 38 3.79 9 3.84 19 3.84 29 3.98 39 3.85 10 3.80 20 3.87 30 3.96

a. Construct an x¯ - chart for this process with three-sigma limits. Is the process in control?

b. Analyze the data using a median run test and an up/down run test. What can you conclude? LO.1