Final answer:
(a) The null hypothesis
suggests that James' strikeout rate using the new stance is equal to his historical rate of 12.5%. The alternative hypothesis
indicates that James aims to reduce his strikeout rate, making it less than 12.5%.
(b) After conducting a one-proportion hypothesis test in Excel, the test statistic (z) is calculated to be approximately -0.973, and the p-value is about 0.163, rounded to three decimal places.
Step-by-step explanation:
James conducts a one-proportion hypothesis test to examine if his new batting stance has a significant effect on reducing his strikeout rate against left-handed pitchers. The null hypothesis
assumes that the proportion p of strikeouts remains at 12.5%, while the alternative hypothesis
suggests that p is less than 12.5%, reflecting James' desire to improve.
To perform the test, James collects data from 200 simulated at-bats, resulting in 16 strikeouts. Using Excel or statistical software, the test statistic z is computed by comparing the observed proportion of strikeouts to the expected proportion under the null hypothesis. The negative value of z indicates that the observed proportion is less than expected, aligning with James' goal.
The p-value, the probability of obtaining results as extreme as observed under the null hypothesis, is calculated. In this case, the p-value of 0.163 is greater than the significance level of 0.05, suggesting that there is not enough evidence to reject the null hypothesis. James may not have successfully reduced his strikeout rate with the new batting stance based on the current data.