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) A one-sample z-test for a population mean
b) A one-sample t-test for a sample mean
c) A one-sample z-test for a population proportion
d) A matched-pairs t-test for a mean difference
e) A two-sample t-test for a difference between means

Respuesta :

Answer:

d) A matched-pairs t-test for a mean difference

Step-by-step explanation:

The appropriate test for the company's investigation is a matched-pairs t-test for a mean difference.

A matched-pairs t-test is a test that is used to test if compared datasets have significant mean difference.

In this case, the travel company wants to compare the cost for the month of January of the present year, and the cost for the month of January of the previous year for different hotels selected at random.

The travel company also takes the difference in cost of all samples.

You can use the fact that a z test is used if the sample size is bigger or equal to 30 else we use t test.

The appropriate test for the company's investment is given by:

Option d) A matched-pairs t-test for a mean difference

When to use the matched pair t test and when to use the t test?

When there has to be done comparison between means of two sets of paired data, then we use matched pair t test.

How to choose what test is appropriate for the company's investigation?

Since the company recorded the mean cost of one night stay for January of previous year and January of current year for same 31 hotels, thus the data is paired and the mean cost has to be compared (whether the cost increased after one year or not). Thus, the appropriate choice for the company will be the matched pair t-test.

Thus,

The appropriate test for the company's investment is given by:

Option d) A matched-pairs t-test for a mean difference

Learn more about one-sample z-test here:

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