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		40		14		$	1,425		31
2			1,361		20		15			1,445		51
3			1,426		21		16			1,439		62
4			1,470		54		17			1,348		45
5			1,456		62		18			1,450		41
6			1,430		29		19			1,431		62
7			1,354		22		20			1,446		47
8			1,442		21		21			1,485		43
9			1,394		15		22			1,405		38
10			1,459		65		23			1,461		36
11			1,399		41		24			1,490		61
12			1,458		35		25			1,426		65
13			1,537		51
Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.) c-1. State the decision rule for 0.025 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.) c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.02 significance level. 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.)

Answer 1

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.464

c-1)

Decision rule: reject Ho if test statistic t>2.069

c-2)

test stat t=

r*(√(n-2)/(1-r2))=

2.51

c-3)

yes since test statistic falls in rejection region

21.5% of the variation in revenue in the restaurant is accounted for by the number of rooms occupied