Question

The marketing brochure for a travel agency shows that the standard deviation of hotel room rates for two cities is the same. Table 7is given the per day room rate in Pak Rs.

CITY 1 PER DAY ROOM RATE (PKR)	12000	12500	15000	14000	17000
CITY 2 PER DAY ROOM RATE (PKR)	13000	14000	18000	11000	15000

Can you reject the agency claim at α=0.05

Answer 1

Solution :

The null and alternative hypotheses would be as follows :

i.e. The population standard deviations of the hotel room rates for two cities are equal.

i.e. The population standard deviations of the hotel room rates for two cities are not equal.

To test the hypothesis the most appropriate test is F test for testing the equality of two population variances. The test statistic is given as follows :

Where, are sample variances.

The test statistic follows F distribution with (n​​​​​​1 - 1, n​​​​​​2 - 1) degrees of freedom. n1, n2 are sample sizes.

We have, n1 = 5, n2 = 5

The value of the test statistic is 0.6045

Degrees of freedom = (5 - 1, 5 - 1) = (4, 4)

Since our test is two-tailed test, therefore we shall obtain two-tailed critical values of F at given significance level.

Level of significance = 0.05

The two-tailed critical values of F at 0.05 significance level and (4, 4) degrees of freedom is given as follows :

Critical values = 0.1041 and 9.6045

For two-tailed F test we make decision rule as follows :

We reject the null hypothesis (H​​​​​​0) if value of test statisic does not lie between the two-tailed Critical values of F.

We fail to reject the null hypothesis (H​​​​​​0) if value of test statisic lies between the two-tailed Critical values of F.

Test statisic value = 0.6045

Critical values = 0.1041 and 9.6045

Since, value of the test statistic lies between the two-tailed critical values of F, therefore we shall be fail to reject the null hypothesis (H​​​​​​0) at 0.05 significance level.

Conclusion : At 0.05 significance level, there is not sufficient evidence to reject the agency claim.