Index (Model Type Index)	Eng Displ	# Cyl	Transmission	City Fuel Efficiency	highway Fuel Efficiency	Transmission (Auto, Manual)
562	2	4	Auto(A8)	22	24	Auto
49	2.9	6	Auto(S8)	18	28	Auto
118	2	4	Auto(A9)	22	31	Auto
315	2.5	4	Auto(S6)	23	32	Auto
181	5	8	Auto(S8)	16	24	Auto
126	2.5	4	Auto(S8)	25	32	Auto
45	2	4	Auto(A8)	22	31	Auto
12	2	4	Auto(AV-S10)	31	38	Auto
555	2	4	Auto(A9)	21	29	Auto
140	3.4	6	Auto(S10)	18	24	Auto
127	2	4	Auto(A9)	21	30	Auto
852	4.4	8	Auto(S8)	17	24	Auto
148	2.3	4	Auto(S10)	20	21	Auto
874	6.2	8	Auto(A10)	14	20	Auto
39	2.5	4	Auto(AV-S6)	43	43	Auto
232	2.5	4	Auto(AM-S7)	19	25	Auto
225	3.5	6	Auto(S10)	15	18	Auto
4	1.8	4	Auto(AV)	53	52	Auto
210	2	4	Auto(AM8)	20	28	Auto
541	2	4	Auto(S9)	21	26	Auto
862	6.2	8	Auto(A10)	14	19	Auto

The dataset Fuel contains information on fuel economy, in miles per gallon, published by the U.S. Department of Energy for a random sample of 20 cars manufactured in 2022².

a) Create a side-by-side boxplot to examine the distribution of city fuel efficiency by transmission type (auto or manual). Comment on the normality of the distributions and on any differences you observe between them. Use software to find the corresponding mean and standard deviation values.

b) Carry out manually an appropriate parametric hypothesis test to determine whether there exists a difference in mean city fuel efficiency between cars with manual and automatic transmissions. Assume that the city fuel efficiencies for manual and automatic cars are approximately normally distributed, the two population variances are unequal, and use a 5% significance level. Use statistical software to obtain the corresponding degrees of freedom and to confirm your results.

c) Confirm the conclusion obtained from the hypothesis test in part b) by manually constructing the corresponding 95% confidence interval for the mean difference in city fuel efficiency between cars with manual and automatic transmissions. Use statistical software to check your results and explain your answer.