Question

In: Statistics and Probability

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested...

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.

Solutions

Expert Solution

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


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