The mean waiting time at the drivethrough of a fastfood restaurant from the time an order is placed to the time the order is received is 87.9 seconds. A manager devises a new drivethrough system that he believes will decrease wait time. As a test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below.
102.7
67.0
56.8
76.4
67.6
82.1
93.8
85.6
72.6
85.4
Critical values
Sample Size, n 
Critical Value 
Sample Size, n 
Critical Value 


5 
0.880 
16 
0.941 

6 
0.888 
17 
0.944 

7 
0.898 
18 
0.946 

8 
0.906 
19 
0.949 

9 
0.912 
20 
0.951 

10 
0.918 
21 
0.952 

11 
0.923 
22 
0.954 

12 
0.928 
23 
0.956 

13 
0.932 
24 
0.957 

14 
0.935 
25 
0.959 

15 
0.939 
30 
0.960 
(a) Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r=0.993.
Are the conditions for testing the hypothesis satisfied?
▼ Yes, No, the conditions▼ are not are satisfied. The normal probability plot▼ is not is linear enough, since the correlation coefficient is▼ greater less than the critical value. 
(b) Is the new system effective? Conduct a hypothesis test using the Pvalue approach and a level of significance of
alpha equals 0.01α=0.01.
First determine the appropriate hypotheses.
H0:
▼
p
σ
μ
▼
=
<
>
≠
87.9
H1:
▼
σ
p
μ
▼
>
<
=
≠
87.9
Find the test statistic.
t0=__?__
Find the Pvalue.
The Pvalue is
__?__ .
(Round to three decimal places as needed.)
Use the α=0.01 level of significance. What can be concluded from the hypothesis test?
A.
The Pvalue is less than the level of significance so there is not sufficient evidence to conclude the new system is effective.
B.
The Pvalue is greater than the level of significance so there is sufficient evidence to conclude the new system is effective.
C.
The Pvalue is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective.
D.
The Pvalue is less than the level of significance so there is sufficient evidence to conclude the new system is effective.
(a)
Critical value for n=10 is 0.918 and sample correlation coefficient, r=0.993
so r> Critical value so
Yes, the conditions are satisfied. The normal probability plot is linear enough, since the correlation coefficient is greater than the critical value.
(b)
Option C. The Pvalue is greater than the level of significance so there is not sufficient evidence to conclude the new system is effective.
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