Suppose engineers are designing a new baseball bat to replace a company's older model. An experiment was done where shots were hit independently with the new model and the old model using a robotic arm to simulate "standard" conditions. Let 1 be the true mean distance of the new model and 2 be the true mean distance of the old model. The following is the collected data of the shot distances (in yds). (Assume Sample sizes are large for normal-based tests) The model mean std. dev n New x1 = 293.3 s1 = 8.1 n1 = 45 Old x2 = 288.2 s2 = 10.2 n2 = 40

(a) Consider a hypothesis test to test whether the true mean distance of the new model is different than 290 yds.

i. Give the null and alternative hypotheses.

ii. Calculate the test statistic.

iii. Calculate the pvalue. Give your decision and conclusion.

(b) Consider a hypothesis test to test whether new model hits farther than the old model on average.

i. State the null and alternative hypotheses.

ii. Calculate the test statistic.

iii. Calculate the pvalue. Give your decision and conclusion