After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a \( 1 \% \) level of significance, test the claim that the amount contributed to the library fund is independent of ethnic group. \begin{tabular}{|l|c|c|c|c|c|c|} \hline & \multicolumn{6}{c}{ Number of People Making Contribution } \\ \cline { 2 - 6 } Ethnic Group & \( \mathbf{\$ 1 - 5 0} \) & \( \mathbf{\$ 1 - 1 0 0} \) & \( \mathbf{\$ 1 0 1 - 1 5 0} \) & \( \mathbf{\$ 1 5 1 - 2 0 0} \) & Over \( \mathbf{\$ 2 0 0} \) & Row Total \\ \hline A & 81 & 67 & 44 & 40 & 19 & 251 \\ \hline B & 100 & 55 & 56 & 30 & 23 & 264 \\ \hline C & 81 & 60 & 52 & 40 & 33 & 266 \\ \hline D & 105 & 81 & 64 & 58 & 32 & 340 \\ \hline Column Total & 367 & 263 & 216 & 168 & 107 & 1121 \\ \hline \end{tabular} USE SALT (a) What is the level of significance? \( \square \) State the null and alternate hypotheses. \( H_{0}: \) Contribution level and ethnic group are not independent. \( H_{1} \) : Contribution level and ethnic group are not independent. \( H_{0} \) : Contribution level and ethnic group are independent. \( H_{1} \) : Contribution level and ethnic group are independent. \( H_{0} \) : Contribution level and ethnic group are independent. \( H_{1} \) : Contribution level and ethnic group are not independent. \( H_{0} \) : Contribution level and ethnic group are not independent. \( H_{1} \) : Contribution level and ethnic group are independent.
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The level of significance given in the problem is \(1\%\). This is the probability threshold below which we will reject the null hypothesis. Show more…
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