A Web-based retailer wishes to measure whether pay-per-click advertising using Google AdWords results in higher daily sales. To do so, it signs up for an 80-day free trial period.
a) In the first 80 days of using AdWords, the retailer had average sales of $350,000 per day, with a standard deviation of $25,000. Given the sample evidence, compute the 95% and 99% confidence intervals for μ, the average daily sales revenue using AdWords.
b) Before using AdWords, the retailer had an average sales revenue of $345,000 per day. Is the sample evidence sufficient to conclude that the daily sales revenue has increased? To answer this question, perform a hypothesis test at α = .05. State the alternative and null hypotheses, compute the observed significance level (p-value), and state the conclusion of your test. What assumptions are necessary for the inferences of parts a and b to be valid?
c) In the first 20 days of using AdWords, the retailer had average sales of $375,000 per day, with a standard deviation of $27,000. Using only the sample evidence from these 20 days, compute the 95% and 99% confidence intervals for μ, the average daily sales revenue using AdWords.
d) Is the sample evidence from these 20 days sufficient to conclude that the daily sales revenue has increased from the historical mean of $345,000 per day? To answer this question, perform a hypothesis test at α = .05. State the alternative and null hypotheses, compute the observed significance level (p-value), and state the conclusion of your test. What assumptions are necessary for the inferences of parts c and d to be valid?
e) The retailer has the option of extending its AdWords subscription beyond the 80-day free trial period. Based on all of the sample evidence, should the retailer continue using AdWords? Explain your answer, and resolve any apparent contradictions with your answers to parts b and d. (Hint: has the daily revenue stayed constant over time?)