Final answer:
To determine if Will is 32 seconds faster than Andrew in swimming, we would conduct a hypothesis test, similar to how we concluded Jeffrey swims faster with new goggles. We would need the swim times for Will and Andrew, and using a calculator like the TI-83, we would calculate a p-value to make a conclusion at the 5 percent significance level.
Step-by-step explanation:
The question 'Determine if each statement is true will swan 32 seconds faster than andrew' prompts us to conduct a statistical analysis to validate the claim about Will Swan's swimming speed compared to Andrew. This analysis falls under the domain of hypothesis testing, a fundamental concept in statistics commonly covered in high school Mathematics.
Given that we have a conclusion explaining that Jeffrey swims faster using new goggles with a mean time less than 16.43 seconds at a 5 percent significance level, we can use a similar approach to test Will's speed against Andrew's. To do this correctly, we would need data involving Will and Andrew's swim times and possibly perform a t-test or z-test, which could be computed using statistical software or a graphing calculator like the TI-83 or higher.
The p-value is a critical part of this analysis, as it indicates the probability of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. A low p-value, typically less than the chosen significance level (alpha), suggests that we reject the null hypothesis in favor of the alternative hypothesis. In this context, if the obtained p-value is less than 0.05 (the 5 percent significance level), we may conclude that Will is indeed faster than Andrew by 32 seconds. Without the actual data, we cannot perform the calculation, but these are the steps and the statistical methodology required to reach a conclusion.