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# Essay topic: Statistical decisions

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In the last case you reviewed chapters 1 – 3 material and also applied your knowledge of chapter 8 material (estimation). I’d like for you to use the same dataset, but this time apply chapter 9 material (hypothesis testing).

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As a reminder: On page 28 – 29 of your text you will find the description of a data set for a company that sells three different levels of treadmills (as well as other exercise equipment).

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1) Download a clean copy of the file CardioGoodFitness.xlsx to your computer. Remember, don’t try to work on it by just clicking on the file name from Blackboard. You need to save it first.

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2) Years ago the company did an analysis of their entire customer base and found that the average income for their customers was \$50,000. They believe that incomes of their current customers are significantly higher than that. Test at the 10% significance level, showing all steps of the hypothesis testing procedure (see the text, page 307). Be sure to include a practical statement indicating how the company could use the results you’ve found. HINT: here are the steps to follow…

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· Write your Ho and H1

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· Make note of your alpha (level of significance)

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· Determine your test statistic (that is, find the proper formula to use)

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· Find the critical value of the test statistic from the table, and define your rejection region

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· Find your sample mean and standard deviation using the proper Excel formulas. Compute the value of the test statistic (that is, do the number crunching in the formula you identified in the third step)

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· Make the statistical decision and interpret in practical form

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3) Years ago about 30% of purchases were for the TM 798 (the “high end” expensive treadmill), however since those data were collected we’ve gone through a recession, and a lot of people’s finances haven’t really recovered. Has the proportion of people purchasing the TM 798 dropped significantly? Test at the 5% level of significance. Be sure to include a practical statement indicating how the company could use the results you’ve found.

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That’s it! The final case (for chapter 13) will use the same data set but will focus on relationships between variables.

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