The mean waiting time at the drive-through of a fast-food restaurant from the ti

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

(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=0.985. Are the conditions for testing the hypothesis satisfied?

Yes or No, the conditions are are or are not satisfied. The normal probability plot is or is not linear enough, since the correlation coefficient is less or greater than the critical value.

60 75 90 105 -2 -1 0 1 2 Time (sec) Expected z-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 (94, 1). All coordinates are approximate.

(b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of alpha equals 0.1.

First determine the appropriate hypotheses.

Upper H 0: mu p sigma equals greater than not equals less than 88.3

Upper H 1: p mu sigma equals less than not equals greater than 88.3

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 alpha equals 0.1 level of significance. What can be concluded from the hypothesis test?

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

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

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

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

Explanation / Answer

a)

Answer B : Yes, the conditions are satisfied. ( i.e Normal population , Small sample , Unknown sd)

b)

H0 : µ = 87.5

H1 : µ < 87.5

Sample Mean = 80

Sample SD = 14.38966

Test Static (t0) = (x µ0) / ( s / sqrt(n))

= (80 87.5)/( 14.39 / sqrt(10))

= 1.65 Answer

dF = 10-1 = 9

alpha =0.01

Therefore,

P-Value = 0.067 Answer

Conclusion:

Answer A.

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