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		Revenue			Occupied		Day		Revenue			Occupied
1		$	1,452		15		14		$	1,425		65
2			1,361		20		15			1,445		51
3			1,426		21		16			1,439		62
4			1,470		15		17			1,348		45
5			1,456		37		18			1,450		41
6			1,430		29		19			1,431		62
7			1,354		23		20			1,446		47
8			1,442		15		21			1,485		43
9			1,394		58		22			1,405		38
10			1,459		62		23			1,461		51
11			1,399		74		24			1,490		61
12			1,458		88		25			1,426		39
13			1,537		62

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

Pearson Correlation:

2.

c-1. 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 >.

c-2. Compute the value of the test statistic.

	Value of the test statistic

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

1)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.223

2)

Decision rule: reject Ho if test statistic t>2.500

c-2)

test stat t=

r*(√(n-2)/(1-r2))=

1.096

d)

5.0 % of the variation in revenue is explained by variation in occupied room