A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.
|
Day |
Income |
Occupied |
|
1 |
$1,452 |
23 |
|
2 |
1,361 |
47 |
|
3 |
1,426 |
21 |
|
4 |
1,470 |
39 |
|
5 |
1,456 |
37 |
|
6 |
1,430 |
29 |
|
7 |
1,354 |
23 |
|
8 |
1,442 |
44 |
|
9 |
1,394 |
45 |
|
10 |
1,459 |
16 |
|
11 |
1,399 |
30 |
|
12 |
1,458 |
42 |
|
13 |
1,537 |
54 |
|
14 |
$1,425 |
27 |
|
15 |
1,445 |
34 |
|
16 |
1,439 |
15 |
|
17 |
1,348 |
19 |
|
18 |
1,450 |
38 |
|
19 |
1,431 |
44 |
|
20 |
1,446 |
47 |
|
21 |
1,485 |
43 |
|
22 |
1,405 |
38 |
|
23 |
1,461 |
51 |
|
24 |
1,490 |
61 |
|
25 |
1,426 |
39 |
Use a statistical software package to answer the following questions.
a. Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.
b. Determine the coefficient of correlation between the two variables. Interpret the value.
c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.
d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?
Answer
(A)
(B)
r = 0.44, there is a WEAK positive correlation.
(C)
df = n-2 = 25-2 = 23
α = 0.05
one-tailed critical value T = 1.319
Test statistic T = r*Sqrt[(n-2)/(1-r²)] = 0.44*Sqrt[(25-2)/(1-0.44²)] = 2.35
Conclusion: Since 2.35 > 1.319 we conclude that there is a positive relationship between the variables.
(D)
r² = 0.44² = 0.1936, so approximately 19% of the variation in revenue is explained by the variation in the number of rooms occupied.