Question

The manager of a Barrier Reef resort wished to know the major determinants of the average daily expenditure by tourists (measured in dollars). From interviews with 16 tourists who have stayed at Great Barrier Reef holiday resorts, data on the size of the group, the length of stay in the region (measured in days), the number of resorts visited and the number of holidays they have had in the last five years. The partially completed ANOVA table for the regression model using all the variables on which data was collected is given below:

Source of variation	df	SS	MS
Regression	A	D	F
Error	B	E	242.7
Total	C	13594.4

Assume that a 0.005 level of significance has been adopted for the test of the overall significance of the relationship.

1. Calculate the test statistic, reporting your answer correct to two decimal places.  
2. Use the tables in the text to determine the critical value for the test.  
3. Is the null hypothesis rejected for this test? Type yes or no.  
4. Hence, on the basis of this test, is at least one of group size, the length of stay, the number of resorts visited and the number of holidays taken related to average daily expenditure by tourists? Type yes or no.

Answer 1

Answer :

Given that :

No.of tourists n = 16

From the table

Source of variation	DF	SS	MS
Regression	= 5 - 1 = 4	= 13594.9 - 2669.7 = 10924.7	= 10924.7 / 4 = 2731.175
Error	= 16 - 5 = 11	= 11 * 242.7 = 2669.7	242.7
Total	= 11+4 = 15	13594.4

1)Test statistic F = MS Regression / MS error

= 2731.175 / 242.7

= 11.25

F = 11.25

2)From the F critical value table :

F critical value = 6.8809

3)YES

The null hypothesis is rejected.

4)YES