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 84.3 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.

103.8

68.1

57.2

76.0

64.8

80.7

93.3

86.3

71.8

78.0

SampleSize n Critical Value

5 .880

6 .888

7 .898

8 .906

9 .912

10 .918

11 .923

12 .928

13 .932

14 .935

15 .939

16 .941

17 .944

18 .946

19 .949

20 .951

21 .952

22 .954

23 .956

24 .957

25 .959

30 .960

(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 =0.992. Are the conditions for testing the hypothesissatisfied?

______ the conditions ______ satisfied. The normal probability plot _____ linear enough, since the correlation is ____ than the critical value.

(b) Is the new systemeffective? Conduct a hypothesis test using theP-value approach and a level of significance of =0.05.

First determine the appropriate hypotheses.

H0:

H1:

find the test statistic.

t0 = ____ (rounding to two decimal places)

find the P value: ____ (rounding to three decimal places)

Use the =0.05 level of significance. What can be concluded from the hypothesistest?