Final answer:
In hypothesis testing, one tests a claim about a population mean by setting up null and alternative hypotheses and choosing a significance level. A test statistic is calculated and compared to critical values or assessed by its p-value. If the p-value is less than the significance level, the null hypothesis is rejected in favor of the alternative.
Step-by-step explanation:
To test the claim that the mean of all taxi cab ride times in New York City yellow cabs on a Friday morning is less than a certain value, a hypothesis test can be performed. The claim here is a statement about the population mean (μ), and the hypothesis testing procedure follows a set pattern: stating null and alternative hypotheses, choosing a significance level (α), calculating a test statistic, and comparing this statistic with a critical value or using a p-value to make a decision.
For example, if we want to test the hypothesis at a 5 percent significance level (0.05), the null hypothesis (H0) would state that the mean time is equal to some value (μ = μ0), while the alternative hypothesis (H1) would claim that the mean time is less than this value (μ < μ0). Once the test statistic is calculated, typically using a t-test or a z-test depending on sample size and variance knowledge, the p-value associated with that test statistic indicates the probability of observing a result as extreme as, or more extreme than, the one obtained assuming the null hypothesis is true.
If the p-value is less than the chosen significance level, the null hypothesis is rejected in favor of the alternative hypothesis. The decision to reject or not reject the null hypothesis is based on this comparison. For instance, if the p-value is 0.02 and the significance level is 0.05, we would reject the null hypothesis, concluding that there is sufficient evidence to support the claim that the mean time is less than the specified value.