Math 533 Project B

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Math 533 Course Project: AJ DAVIS DEPARTMENT STORES Project Part B: Hypothesis Testing and Confidence Intervals Summary Report In order to calculate the probability of each situation hypothesis tests were administered on each scenario. In summary, hypothesis testing is used to check whether there is or is not likely to be a difference between one or more data sets. In statistics there is no such thing as 100% sure so uncertainty must be allowed. Instead the best thing we can do in statistics is to show things are false to make the best inferences. The following information below describes what was concluded from the hypothesis tests below. Lastly, the following interpretations were found by analyzing and testing the data attached to the docsharing excel file. A. The average (mean) annual income was less than $50,000. There is a very low probability (5% at most) that the annual income for the data from AJ DAVIS is less than $50,000. The way that we concluded this was to test the probability that the annual income of our customers is $50,000 versus the probability that the average annual income was less than $50,000. What we found was that there is a 95% chance that the average annual income of our customers is between $69,997.9 and $70,001.8. This was also backed with a p-value (which determines the strength of the evidence) that showed weak evidence against the average income equaling $50,000. Since we cannot deny that the annual income average is $50,000, we have no choice but to keep it as a consideration moving forward. B. The true population proportion of customers who live in an urban area exceeds 40%. Scenario B is very similar to scenario A because we were able to indicate a weak p-value to indicate that the population proportion of urban customers could be exactly 40%. With hypothesis testing we were able to test the probability of
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