Question

A study by W. F. Woodward in 1970 explored whether taking a "narrow angle" or a "wide angle" while rounding first base would increase your time to second base. Narrow angle Wide angle In Woodward's study, he used a stopwatch to time 22 different runners going from a spot 35 feet past home to a spot 15 feet before second. He had each runner use each method, with a rest period in between. Here are the summary statistics on the difference in times (narrow wide) for the 22 players: Sample Sample size |average (kcal)| Sample SD (kcal) Sd -0.0992 Difference Narrow Wide22Ed0.0803 s

Answer 1

$t=0.0803/(0.0992/\sqrt{22})=3.80\\ Since~standardized~value~is~greater~than~3~hence~it~is~an~outlier~and\\ P(t>3.80|t\sim t_{21})=0.0005~hence~the~difference~is~significantly~greater~than~zero\\ hence~finding~of~W.F.~Woodward~is~statistically~significant.\\ \bar{x}_d-2\times \frac{s_d} {\sqrt{n}}=0.0803-2*(0.0992/\sqrt{22})=0.04\\ \bar{x}_d+2\times \frac{s_d}{\sqrt{n}}=0.0803+2*(0.0992/\sqrt{22})=0.12\\ Confidence~interval=(0.04,0.12)$