Question

We considered the mean waiting time at the drive-through of a fast-food restaurant. In addition to concern about the amount of time cars spend in the drive-through, the manager is also worried about the variability in wait times. Prior to the new drive-through system, the standard deviation of wait times was 18.0 seconds. Use the data in the table below to decide whether there is evidence to suggest the standard deviation wait-time is less than 18.0 seconds. Recall that in Homework 1-3, we verified this data could have come from a population that is normally distributed. Use the α = 0.05 level of significance.

108.5	67.4	58.0	75.9	65.1
80.4	95.5	86.3	70.9	72.0

On a separate sheet of paper, write down the hypotheses (H₀ and H_a) to be tested.

Conditions:
a. The χ² ("chi-square") test for standard deviations_______ (is / is not) appropriate for this data.

Rejection Region:
b. To test the given hypotheses, we will use a (left / right / two)________ -tailed test.  
The appropriate critical value(s) for this test is/are______ .  (Report your answer exactly as it appears in Table VII. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

The test statistic for this test is χ²₀=.  (Calculate this value in a single step in your calculator, and report your answer rounded to 3 decimal places.)

c. We ______(reject / fail to reject) H₀.
d. The given data _______ (does / does not) provide significant evidence that the standard deviation of wait times under the new method is less than 18.0 seconds.

Answer 1