The average number of orders per day at a small local restaurant was 40 in the previous years. The management of
the restaurant spent a considerable amount of money on advertising during the last end-of-the-year holiday season. To test if the expensive advertising campaign is effective, the number of orders per day for the first 61 business days of the new year were recorded in the file below.
(a) Do the data support the claim that advertising increases the average number of orders per day? State the appropriate pair of hypotheses, find the test statistic, and give the P-value.
(b) Is the result significant at the = 0.10 level? At = 0.05? At = 0.01? What conclusion should be reached with respect to the null hypothesis?
(c) Does your answer in (b) require the number of orders per day to be normally distributed?
(d) Referring to your answer in (b), which of the two statistical errors might have been made in this case? What does that error mean in this situation?
(e) Find a 90% confidence interval for the mean daily number of orders. What is the margin of error? (
f) How large a sample is required for you to be 90% sure that the estimate of the mean daily number of orders is accurate within 2 orders?
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