The mean waiting time at thedrive-through of afast-food restaurant from the time an order is placed to the time the order is received is 84.2 seconds. A manager devises a newdrive-through system that he believes will decrease wait time. As atest, 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.

101.9

81.0

69.0

95.3

58.6

87.5

76.5

69.0

67.4

83.8

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Click the icon to view the table of correlation coefficient critical values.

(a) Because the sample size issmall, 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=0.988. Are the conditions for testing the hypothesissatisfied?

Yes,

No,

the conditions

are not

are

satisfied. The normal probability plot

is not

is

linearenough, since the correlation coefficient is

less

greater

than the critical value. Inaddition, a boxplot does not show any outliers.

60

75

90

105

-2

-1

0

1

2

Time(sec)

Expectedz-score

A normal probability plot has a horizontal axis labeled Time (seconds) from 50 to 115 in increments of 5 and a vertical axis labeled Expected z-score from negative 2 to 2 in increments of 0.5. Ten plotted points closely follow the pattern of a line that rises from left to right through (58.5, negative 1.55) and (95.5, 1). All coordinates are approximate.

(b) Is the new systemeffective? Conduct a hypothesis test using theP-value approach and a level of significance of =0.01.

First determine the appropriate hypotheses.

H0:

p

p

sigma

mu

less than

<

not equals

equals

=

greater than

>

84.2

H1:

sigma

mu

p

p

less than

<

not equals

equals

=

greater than

>

84.2

Find the test statistic.

t0=

nothing

(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is

nothing

.

(Round to three decimal places asneeded.)

Use the =0.01 level of significance. What can be concluded from the hypothesistest?

A.

TheP-value is less than the level of significance so there issufficient evidence to conclude the new system is effective.

B.

TheP-value is less than the level of significance so there isnotsufficient evidence to conclude the new system is effective.

C.

TheP-value is greater than the level of significance so there isnotsufficient evidence to conclude the new system is effective.

D.

TheP-value is greater than the level of significance so there issufficient evidence to conclude the new system is effect