Question

A. 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 84.3 seconds. A manager devises a new drive-through system that he believes will decrease wait time. He initiates the new system at his restaurant and measures the wait time for ten randomly selected orders. The wait times are provided in the table below. Based on the given data, is the new system effective? Use the α = 0.10 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:
Use Minitab Express to perform a normality test on the given data.
The P-value for the Anderson-Darling test of normality is_____  (Round to 3 decimal places.)
Based on both the normal probability plot and this P-value, the t-test for means  (is / is not)________ valid for the given data.

Rejection Region:
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 VI. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

B. Refer to the data and Minitab Express output from Part A. Note that a table of summary statistics for the given data appears beneath the normal probability plot in Minitab Express. Summary statistics can also be calculated in Minitab Express via Descriptive Statistics -> Describe.

The sample mean wait time is____ seconds. (Round to 3 decimal places.)
The sample standard deviation of wait times is_____ seconds.  (Round to 3 decimal places.)
The test statistic for this test is t₀=______.  (Calculate this value in a single step in your calculator using the rounded sample statistics reported above, and report your answer rounded to 3 decimal places.)

Label the test statistic in your sketch from Question 6. Use this sketch to conclude the hypothesis test.

We______ (reject / fail to reject) H₀.
The given data_____ (does / does not) provide significant evidence that the new drive-through system is effective in reducing the mean reducing wait time.

Answer 1