The mean waiting time at the drivethrough of a fastfood rest

The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 87.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table. Complete parts (a) and (b) below. Because the sample size is small the manager must verify that the wait time is normally distributed and the sample does not contain any others. The normal probability plot and box plot are shown. Are the conditions for testing the hypothesis satisfied?

Solution

a)

Answer B : Yes, the conditions are satisfied. ( i.e Normal population , Small sample , Unknown sd)

b)

H0 : µ = 87.5

H1 : µ < 87.5

Sample Mean = 80

Sample SD = 14.38966

Test Static (t₀) = (x µ0) / ( s / sqrt(n))

= (80 87.5)/( 14.39 / sqrt(10))

= 1.65 Answer

dF = 10-1 = 9

alpha =0.01

Therefore,

P-Value = 0.067 Answer

Conclusion:

Answer A.