Question

The mean waiting time at the​ drive-through of a​ fast-food restaurant from the time an order...

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 85.3 seconds. A manager devises a new​ drive-through system that she she believes will decrease wait time. As a​ test, she she initiates the new system at her her 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.

101.3
68.9
57.4
73.5
67.3
81.4
96.0
84.7
69.2
80.3

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=0.981.

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​ P-value approach and a level of significance of α=0.05.

First determine the appropriate hypotheses.

H0​:

p

μ

σ

=

>

<

85.3

H1​:

μ

p

σ

<

>

85.3

Find the test statistic.

t0=__?__

​(Round to two decimal places as​ needed.)

Find the​ P-value.

The​ P-value is __?__.

​(Round to three decimal places as​ needed.)

Use the α=0.05 level of significance. What can be concluded from the hypothesis​ test?

A.

The​ P-value is greater than the level of significance so there not sufficient evidence to conclude the new system is effective.

B.

The​ P-value is greater than the level of significance so there sufficient evidence to conclude the new system is effective.

C.

The​ P-value is less than the level of significance so there sufficient evidence to conclude the new system is effective.

D.

The​ P-value is less than the level of significance so there not sufficient evidence to conclude the new system is effective.

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