A reading society allows its members to request books, then pick up their books at the library or have them delivered to their home. Here is the historical data for number of books per year for members who choose each option. Pickup location Mean Std. dev. Total members Library \[15.7\] \[11.3\] \[252\] Home \[13.5\] \[8.1\] \[147\] The society leaders take separate random samples of \[24\] members from each option. They will then look at the difference in their sample means \[\left( \bar{x}_\text{L} - \bar{x}_\text{H} \right)\]. Consider the formula: \[\sigma_{\bar{x}_1-\bar{x}_2}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_\text{2}^2}{n_2}}\] Why is it not appropriate to use this formula for the standard deviation of \[\bar{x}_\text{L}-\bar{x}_\text{H}\]? Choose 1 answer: