An Eco-Friendly Home Improvement Store Owner Is Thinking About Carrying

Essay

An eco-friendly home improvement store owner is thinking about carrying some new products and is interested in her customer's opinions. The shop owner decides to randomly sample 397 customers and ask them whether they have (a) heard about bricks made from recycled materials and (b) whether they have heard of landscaping materials made from recycled glass. She also asked each respondent how often they typically make purchases during a month. The table below shows the results from the study. Assume all conditions for testing have been met. $$\begin{array} { | l | c | c | c | } \hline & 1 - 2 \text { purchases/mo. } & \text { 3+ purchases/mo. } & \text { 5+ purchases/mo. } \\ \hline \text { Recycled bricks, yes? } & 82 & 42 & 72 \\ \hline \text { Recycled bricks, no? } & 44 & 32 & 12 \\ \hline \text { Landscaping glass, yes? } & 23 & 7 & 44 \\ \hline \text { Landscaping glass, no? } & 11 & 18 & 10 \\ \hline \end{array}$$ Test the hypothesis that how the respondents answered the questions is associated with number of monthly purchases, using a significance level of 0.05. State the correct decision regarding the null hypothesis and write a conclusion using a full sentence. Refer to the output below. $$\begin{array} { l } \chi ^ { 2 } - \mathrm { Test } \\X ^ { 2 } = 50.30560555 \\p = 4.0824186 E - 9 \\\mathrm { df } = 6\end{array}$$