Question

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3 [10] 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 89.7 seconds. Amanager 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 below. Is the new system effective? Use an a= 0.1 level of significance. 108.5 80.5 69.8 94.0 58.0 85.6 76.6 72.8 67.8 86.4 (a) Are the conditions for testing the hypothesis satisfied? Explain how you know. (b) State the hypotheses. Clearly define the parameter(s) you are testing. Ho: H: (c) Perform the test. Clearly state the test used, the P-value, and the outcome of the test. Test used: P-value: Outcome (circle one): Reject Ho Do not reject Ho (d) State the conclusion. Be sure to relate your answer to the context of this problem.

Answer 1

a)

• In theory, the data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ).
• The data must be reasonably random.
• The sample must be less than 10% of the population.

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 89.7
Alternative Hypothesis, Ha: μ < 89.7

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (80 - 89.7)/(14.4572/sqrt(10))
t = -2.12

P-value Approach
P-value = 0.0315
As P-value < 0.1, reject the null hypothesis.

d)

There is sufficient evidence to conclude that the mean waiting time at the drive through of fast food restaurant is decrease wait time