Major League Baseball is concerned with the possibility of a fan getting hit by
ID: 3272876 • Letter: M
Question
Major League Baseball is concerned with the possibility of a fan getting hit by a broken bat. They would like to switch from using a Maple bat to an Ash bat. They a significant difference between the speed of the baseball off the bat to ensure that the game remains unchanged. A sample of 125 Maple bats had an average ball speed of 113 mph and a standard deviation of 19 mph, and a sample of 100 Ash bats had an average ball speed of 109 mph with a standard deviation of 15 mph. At the 5% significance level test the hypothesis that there is a difference between the mean speed of the ball off the Maple bat compared to the mean speed of the ball off the Ash bat. You may assume that all initial conditions or assumptions are met. Show all necessary steps and be sure to state your conclusion within the context of the problem.Explanation / Answer
Solution:-
x1 = 113, n1 = 125, s1 = 19
x2 = 109, n2 = 100, s2 = 15
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.267
DF = 125 + 100 - 2
D.F = 223
t = [ (x1 - x2) - d ] / SE
t = 1.76
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 223 degrees of freedom is more extreme than -1.76; that is, less than -1.76 or greater than 1.76.
Thus, the P-value = 0.0798
Interpret results. Since the P-value (0.0798) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that there is difference between the mean speed of the ball off the two bats.
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