Question

Leo coaches Little League baseball and uses a pitching machine. He sets the machine so that it should deliver balls at 53mph. He's checking the accuracy one day and did some math: 152 pitches, an average of 54mph with a standard deviation of 4mph. Should he be concerned that the velocity will be significantly different than 53mph? State the

(a) null hypothesis,
(b) alternative hypothesis
(c) test statistic,
(d) p value, and whether to
(e) accept or reject the null with reason.

Answer 1

Leo can test whether the pitching machine delivers balls at a significantly different speed than 53mph by calculating the z-score and p-value.

Step-by-step explanation:

The student's null hypothesis (H0) would be that the pitching machine delivers balls at 53mph, and the alternative hypothesis (H1) would be that the pitching machine delivers balls at a significantly different speed than 53mph.

To test these hypotheses, Leo would need to calculate the test statistic, which in this case would be the z-score. Leo can calculate the z-score using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

The p-value can be obtained by using a z-table or a statistical calculator.

If the p-value is less than the significance level (usually denoted as alpha), Leo would reject the null hypothesis and conclude that the pitching machine delivers balls at a significantly different speed than 53mph.

Otherwise, he would fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant difference in speed.