Final answer:
To predict the distance a football travels based on leg strength, one uses a linear regression analysis to derive an equation. The regression equation is then used to substitute the leg strength value to predict distance. A hypothesis test can further analyze improvements such as the change in throwing distance due to grip adjustments.
Step-by-step explanation:
To predict the distance traveled by a football based on the thrower's leg strength, we need to establish a linear regression equation based on the given data points. Generally, to find the equation of the form y = mx + b, where y represents the distance and x represents the strength, we need to find the slope (m) and the y-intercept (b). Although the specific regression calculation isn't provided here, once the regression analysis is done and the equation is determined, you would simply substitute x = 175 (for a leg strength of 175 lbs) into the regression equation to predict the corresponding distance.
For the scenario where the mean throwing distance of a football by a high school quarterback is being analyzed for improvement after a grip change: A hypothesis test will involve stating the null hypothesis that the grip change does not increase the throwing distance (H0: μm ≤ 40 yards) and the alternative hypothesis that it does (Ha: μm > 40 yards). With an alpha level of 0.05 and assuming normal distribution, a one-sample t-test will be used to test if the new mean of 45 yards is significantly greater than the original mean of 40 yards.