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		60		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		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		51

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

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

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.)

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

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.

d.

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.)

Answer 1

a)

b)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	60	1452	309.7600	270.27	289.3440
2	20	1361	501.7600	5559.19	1670.1440
3	21	1426	457.9600	91.39	204.5840
4	80	1470	1413.7600	1186.11	1294.9440
5	70	1456	761.7600	417.79	564.1440
6	29	1430	179.5600	30.91	74.5040
7	30	1354	153.7600	6652.03	1011.3440
8	21	1442	457.9600	41.47	-137.8160
9	15	1394	750.7600	1727.23	1138.7440
10	36	1459	40.9600	549.43	-150.0160
11	41	1399	1.9600	1336.63	51.1840
12	35	1458	54.7600	503.55	-166.0560
13	51	1537	73.9600	10290.07	872.3840
14	31	1425	129.9600	111.51	120.3840
15	51	1445	73.9600	89.11	81.1840
16	62	1439	384.1600	11.83	67.4240
17	45	1348	6.7600	7666.75	-227.6560
18	41	1450	1.9600	208.51	-20.2160
19	62	1431	384.1600	20.79	-89.3760
20	47	1446	21.1600	108.99	48.0240
21	43	1485	0.3600	2444.31	29.6640
22	38	1405	19.3600	933.91	134.4640
23	36	1461	40.9600	647.19	-162.8160
24	30	1490	153.7600	2963.71	-675.0560
25	65	1426	510.7600	91.39	-216.0560
Total	1060	35889	6886.0000	43954.16	5807.4000
Mean	42.400	1435.56	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.334

c-1)

0.01 level,right tail test and n-2= 23 df, critical t=			2.4999
Decision rule: reject Ho if test statistic t>2.500

c-2)

test stat t=

r*(√(n-2)/(1-r2))=

1.70

c-3)

No since test statistic is not in rejection region

d)

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

=r²*100 =11.1 %