# Lecture 4 - Contingency Tables Making decisions Who buys...

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Contingency Tables Making decisions

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Who buys Diet Cola? Firm wants to market new diet cola – who is most likely market?
Study Design Random sample of people at different income levels Question: do you buy diet cola?

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Diet Cola and Income: Data Buy Don’t Buy Total Under \$20k 9149 22618 31767 \$20 - \$39K 15691 30324 46015 \$40 - \$59K 13202 25288 38490 \$60 - \$99K 21146 31456 52602 \$100K or more 18121 24718 42839 Total 77309 134404 211713
Which of the following is a null hypothesis? A) Diet cola purchases are not related to income B) The likelihood of purchasing diet cola varies with income level

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Expected Counts Yes No Total Under \$20k 11600 20167 31767 \$20 - \$39K 16802.8 29212.2 46015 \$40 - \$59K 14055 24435 38490 \$60 - \$99K 19208.1 33393.9 52602 \$100K or more 15643.1 27195.9 42839 Total 77309 134404 211713
Expected Counts Formula

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Chi-square statistic 2 ˆ 1939 χ =
What are the degrees of freedom for this statistic?

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At a 5% significance level, we should A) Reject the null hypothesis B) Fail to reject the null hypothesis

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p-value Assume the null hypothesis is true p-value is the probability of observing a value of the sample statistic at least as big as the value we calculated

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Significance level Denoted by α Defines a decision rule for our test

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• Spring '08
• BethIngram
• Statistics, Statistical hypothesis testing, Statistical significance, diet cola

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