Question

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 84.3 seconds. A manager devises a new drive-through system that he believes will decrease wait time. He initiates the new system at his restaurant and measures the wait time for ten randomly selected orders. The wait times are provided in the table below. Based on the given data, is the new system effective? Use the α = 0.10 level of significance.

108.5	67.4	58.0	75.9	65.1
80.4	95.5	86.3	70.9	72.0

a) The sample mean wait time is ______seconds. (Round to 3 decimal places.)
b) The sample standard deviation of wait times is____ seconds.  (Round to 3 decimal places.)
c) The test statistic for this test is t₀= ___.  report your answer rounded to 3 decimal places

d) We __ (reject / fail to reject) H₀.
e) The given data ___ (does / does not) provide significant evidence that the new drive-through system is effective in reducing the mean reducing wait time.

Answer 1

the necessary calculation table:-

wait times (x)	x2
108.5	11772.25
67.4	4542.76
58	3364
75.9	5760.81
65.1	4238.01
80.4	6464.16
95.5	9120.25
86.3	7447.69
70.9	5026.81
72	5184
sum=780	sum=62920.74

a).The sample mean wait time is:-

b).The sample standard deviation of wait times is :-

c).hypothesis:-

[ claim ]

the test statistic for this test be:-

d).df = (n-1) = (10-1 )= 9

p value is:-

[ in any blank cell of excel type =T.DIST(-1.31,9,TRUE)]

decision:-

p value = 0.1113 > 0.10 (alpha)

we reject the null hypothesis.

e).conclusion:-

The given data does not provide significant evidence that the new drive-through system is effective in reducing the mean reducing wait time.

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