Question

A suburban hotel derives its revenue 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			Day	Income				Occupied
1		$	1,452			20		14		$	1,425			31
2			1,361			20		15			1,445			51
3			1,426			21		16			1,439			62
4			1,470			80		17			1,348			45
5			1,456			70		18			1,450			41
6			1,430			29		19			1,431			62
7			1,354			70		20			1,446			47
8			1,442			21		21			1,485			43
9			1,394			15		22			1,405			38
10			1,459			36		23			1,461			36
11			1,399			41		24			1,490			30
12			1,458			35		25			1,426			65
13			1,537			51

  
Click here for the Excel Data File
  

Use a statistical software package to answer the following questions.

b.	Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson correlation

State the decision rule for 0.01 significance level: H0: ρ ≤ 0; H1: ρ > 0 (Round your answer to 3 decimal places.)

Reject H0 if t >

Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

c.	Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

(Click to select)  Reject  Fail to reject  H0, There is a  (Click to select)  no correlation  a negative correlation  a positive correlation  between revenue and occupied rooms.

d.	What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

% of the variation in revenue is explained by variation in occupied rooms.

Answer 1

a)from excel: data data analysis: regression : below is the output:

a)

coefficient of correlation between the two variables r =0.103

Reject H₀ if t > 2.500 (from excel: t.inv(1-0.01,25-2))

  Value of the test statistic =0.50

c)

Fail to reject  H₀, There is no correlation between revenue and occupied rooms.

d)

1.1 % percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied