Question

# A certain golf club manufacturer advertises that its new driver (the club you use to hit...

1. A certain golf club manufacturer advertises that its new driver (the club you use to hit golf balls off the tee) will increase the distance that golfers achieve relative to their current driver. We decide to test this claim by having 15 golfers hit a drive using the new driver, and then hit one using their current driver. Here are the data for 15 people, with yardages using both clubs:
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 New 247 259 248 275 282 307 288 215 221 260 292 198 240 304 295 Current 240 254 238 268 275 301 292 197 203 262 281 189 225 297 274

1. Show a side-by-side boxplot of the driving distances for the current and new drivers as well as the DIFFERENCE between new and current drivers (a total of three boxplots, side-by-side. USING R
2. Conduct a paired t-test to test whether the new driver produces longer drives, on average, when compared to the current driver using .05 as the probability of a Type 1 error. State your hypotheses, and be sure to check the conditions for your test. State the P-value of your test. (Feel free to use R in showing your work - and show your commands and output if using R.)
3. By using a 95% confidence interval, estimate the true difference in length produced by the new driver relative to the current one, and EXPLAIN what this confidence interval means in context of this problem. (Feel free to use R in showing your work - and show your commands and output if using R.)