The dataset Fuel contains information on fuel economy, in miles per gallon, published by the US. Department of Energy for a random sample of mo cars manufactured in 213122 2. a) Create a side-by-side boxplot to examine the distribution of city fuel eiciency by transmission type (auto or manual]. Comment on the normality of the distributions and on any differences you observe between them. Use software to nd the corresponding mean and standard deviation values. 1 https:ffwwwnttlcnoaegovftdo-webf 3 httpeffwww.fueletonornygovegfdownloadshtm| b] Carry out manually an appropriate parametric hypothesis test to determine whether there exists a difference in mean city fuel efciency between cars with manual and automatic transmissions. Assume that the city fuel efciencies for manual and automatic cars are approximately normally distributed, the two population variances are unequal, and use a 5% signicance level. Use statistical software to obtain the corresponding degrees of freedom and to conrm your results. Conrm the conclusion obtained from the hypothesis test in part b} by manually constructing the corresponding 95% condence interval for the mean difference in city fuel efciency between .rs with manual and automatic transmissions. Use statistical software to check your results and explain your