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		65		14		$	1,425		31
2			1,361		20		15			1,445		51
3			1,426		21		16			1,439		62
4			1,470		50		17			1,348		45
5			1,456		70		18			1,450		41
6			1,430		23		19			1,431		62
7			1,354		30		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		65

1. Choose the scatter diagram that best fits the data.

Scatter diagram 1	Scatter diagram 2	Scatter diagram 3

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

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

Pearson correlation _____

1. 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> _____

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

Value of the test statistic _________

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

______ H0, it ______ reasonable to conclude that there is a positive relationship between revenue and occupied rooms.

4. 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 occupied rooms.

Answer 1

a)

b)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.378

c-1_)

0.01 level,right tail test and n-2= 23 df, critical t=

2.500

Decision rule: reject Ho if test statistic t>2.500

c-2)

test stat t=

r*(√(n-2)/(1-r2))=

1.96

c-3)

fail to reject Ho , it is not  reasonable to conclude that there is a positive relationship between revenue and occupied rooms.

d)

14.3 % of the variation in revenue is explained by variation occupied rooms.