A travel company is investigating whether the average cost of a hotel stay in a certain city has increased over the past year. The company recorded the cost of a one-night stay for a Friday night in January of the current year and in the previous year for 31 hotels selected at random. The difference in cost (current year minus previous year) was calculated for each hotel.
Which of the following is the appropriate test for the company’s investigation?
A one-sample z
-test for a population mean
A
A one-sample t
-test for a sample mean
B
A one-sample z
-test for a population proportion
C
A matched-pairs t
-test for a mean difference
D
A two-sample t
-test for a difference between means
E
Is it a matched pair t test for mean difference so D?
Yes, you are correct. The appropriate test for the company's investigation would be a matched-pairs t-test for a mean difference (option D).
A matched-pairs t-test is used when you have paired data, such as in this case where the cost of hotel stays in the current year is compared to the cost of hotel stays in the previous year for the same hotels. The t-test for a mean difference is specifically designed to test if the mean difference between paired observations is significantly different from zero.
To perform a matched-pairs t-test, you would calculate the difference in cost for each pair of observations (current year minus previous year) and then use these differences to determine if there is a significant change in the average cost of a hotel stay.
To summarize, the appropriate test for this investigation is a matched-pairs t-test for a mean difference (option D) because it involves paired data and aims to assess the change in the average cost of a hotel stay in a certain city over the past year.