The American Automobile Association claims that the average daily cost for meals and lodging for vacationing in Texas is larger than the average costs for vacationing in North Carolina. The table below shows the result of a random survey of vacationers in each state. The two samples are independent. Texas North Carolina $$ \begin{aligned} n_{1} &=35 & n_{2} &=50 W \bar{x}_{1} 8=218 & \bar{x}_{2} &=208 s_{1} 8=28 & s_{2} &=15 \end{aligned) $$ (a) Set up the correct hypotheses to test the claim. [3 pts] (b) Find the standardized test statistic. [3 pts] (c) Find the rejection region and state your conclusion at $\alpha=0.01$. [3 pts) SP.DL.2311