Statistics

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A university has an exclusive agreement with the coffee chain Monobeans. Several students and faculty complained about their lack of baked goods. Looking for a better provider of carbs and caffiene, the university management rents out for one trial semester a space within a newly built department to Monobeans' main competitor Old World Blend.

Based on data measured over many years, coffee stores on campus hada mean number of customers of 468.3 per day each, fluctuating with a standard deviation sigma of 207.5. At the end of the trial semester, Old World Blend's newly opened store featured a mean number of customers of 523.7, recorded over 78 business days in the semester.

1. Would you sign a new exclusive agreement with Old World Blend? Consider alpha = 0.05 as a level of significance, and assume that random fluctuations in number of customers may be either above or below Monobeans' average.

2. OWB signed the trial lease contract on the grounds that across the country, their mean number of customers is 11% higher than Monobeans. Given the local market on campus, how much power (1-Beta) did they have to prove their claim by one trial semester?

3. Regardless of how it ended up for OWB (result of question 2): to achieve 80% power, how many semesters of temporary lease would be necessary?

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