Question

A survey claims that the average cost of a hotel room in Atlanta is greater than 69.23. To test this claim, a researcher selects a sample of 30 hotel rooms and finds the average cost is 68.43. Assume the population standard deviation of 3.72. At a 0.05 significance level, is there enough evidence to support the claim that the average cost of a hotel room in Atlanta is greater than 69.23?

Answer 1

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:

1. Null Hypothesis (H0): The average cost of a hotel room in Atlanta is less than or equal to 69.23.
2. Alternative Hypothesis (Ha): The average cost of a hotel room in Atlanta is greater than 69.23.
3. Test Statistic: The test statistic can be calculated using the formula: t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size)).
4. 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.
5. 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.
6. 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.
7. 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.