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 87.9 seconds. A manager devises a new​ drive-through 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​ P-value 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​ P-value.

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

B.

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

C.

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

D.

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

Answer 1

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