Final answer:
The question pertains to performing a hypothesis test in statistics to ascertain if the average room rate at a resort differs from a regional average. A null and alternative hypothesis is established and sample data is used to carry out a t-test or z-test to reach a conclusion.
Step-by-step explanation:
The question focuses on conducting a hypothesis test in statistics to determine whether the average room rate in a specific resort area is different from the known regional average of $82.53. In this scenario, the travel agent would set up both a null hypothesis (H0: The average rate is $82.53) and an alternative hypothesis (H1: The average rate is not $82.53). To perform the test, the travel agent would collect sample data from the resort area, calculate the sample mean and standard deviation, and use this information to determine a test statistic.
The test could be a t-test or z-test, depending on the sample size and whether the population standard deviation is known.
The chosen significance level (commonly 0.05 for a 95% confidence level) will then be used to decide whether to reject the null hypothesis. If the calculated p-value is less than the chosen significance level, the null hypothesis would be rejected, indicating that there is a statistically significant difference between the resort’s average room rate and the regional average rate.