Question

The average cost of a hotel room in NYC is $168 per night. A random sample of 25 hotel rooms resulted in X = $172.50 and s = $15.40. Test the claim at the 0.05 level.

Answer 1

Solution: The null and alternative hypotheses are given below:

Under null hypothesis, the test statistic is:

Where:

is the sample mean resulted from a random sample of size 25.

is the average cost of a hotel room in NYC.

is the sample standard deviation based on a random sample of size 25

is the sample size.

  

Therefore, the test statistic is

Now we need to find the t critical value at 0.05 significance level for Using the t distribution table, we have:

Since the test statistic does not fall in the rejection region, we, therefore, fail to reject the null hypothesis and there is sufficient evidence to conclude that the average cost of a hotel room in NYC is $168 per night.