Joan Has Just Moved into a New Apartment and Wants $\alpha = 0.05$

Essay

Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use $\alpha = 0.05$ .
$\begin{array}{ll}\hline \text { Store 1 } & \text { Store 2 } \\\hline \bar{X}_{1}=\$ 650 & \bar{X}_{2}=\$ 680 \\\sigma_{1}=\$ 43 & \sigma_{2}=\$ 52 \\n_{1}=42 & n_{2}=45\end{array}$