Final answer:
To test whether the average cost of a hotel room in Atlanta is greater than 69.23, a researcher can conduct a one-sample t-test. By calculating the test statistic and the p-value, one can determine if there is enough evidence to support the claim. In this case, the p-value is less than the significance level, indicating that there is enough evidence to support the claim.
Step-by-step explanation:
To test the claim that the average cost of a hotel room in Atlanta is greater than 69.23, a one-sample t-test can be used. Here's how the hypothesis test can be conducted:
- Null Hypothesis (H0): The average cost of a hotel room in Atlanta is less than or equal to 69.23.
- Alternative Hypothesis (Ha): The average cost of a hotel room in Atlanta is greater than 69.23.
- Test Statistic: The test statistic can be calculated using the formula: t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size)).
- Significance Level: Given a significance level of 0.05, this means we want the p-value to be less than 0.05 in order to reject the null hypothesis.
- Calculation: Using the given sample mean of 68.43, population standard deviation of 3.72, and sample size of 30, we can calculate the test statistic. t = (68.43 - 69.23) / (3.72 / sqrt(30)) = -2.72.
- P-value: With a t-statistic of -2.72 and 29 degrees of freedom, the p-value can be determined using a t-table or a statistical calculator. In this case, the p-value is less than 0.05.
- Conclusion: Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. This provides enough evidence to support the claim that the average cost of a hotel room in Atlanta is greater than 69.23.