A suburban hotel derives its revenue from its hotel and restaurant operations. T
ID: 3150570 • Letter: A
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.
Da Income $1,452 1,361 1,426 1,470 1,456 1,430 1,354 1,442 1,394 1,459 1,399 1,458 1,537 Occupied Da Income Occupied 72 20 21 25 70 23 20 39 $1,425 31 51 62 45 1,445 1,439 1,348 1.450 1,431 1.446 1,485 1.405 1,461 1.490 1,426 15 16 4 19 20 21 62 47 43 38 10 23 24 25 50 60 65 12 13 35 Use a statistical software package to answer the following questions b. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.) Pearson correlation State the decision rule for 0.1 significance level Ho: ps 0; H1: > 0 (Round your answer to 3 decimal places.) Reject Ho if t> Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.1 significance level (Click to select) H. There is a (Click to select between revenue and occupied room 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 roomsExplanation / Answer
answer b) using the MS-excel we can get the correlation coefficient between income and occupied=r=0.355
we can test significance of correlation coefficient using t-test
t-critical =t(0.1,23)=1.714
Reject H0 if t>1.714
t=r*sqrt(n-2)/sqrt(1-r2)=0.355*sqrt(23)/sqrt(1-0.355*0.355)=1.821 with 23 df
value of t-statistic=1.821
answer c) since value of t-statistic=1.821 is greater than the critical t=1.714 therefore
it is reasonable to conclude there is positive relationship between revenue and occupied room
answer d) after regressing revenue on room occupied the R2=0.1262
12.62 % of variation in revenue explained by ther occupied room
Income=x occupied=y 1452 72 1361 20 1426 21 1470 25 1456 70 1430 23 1354 20 1442 39 1394 15 1459 50 1399 41 1458 35 1537 41 1425 31 1445 51 1439 62 1348 45 1450 41 1431 62 1446 47 1485 43 1405 38 1461 36 1490 60 1426 65 var= 1758.1664 261.5456 cov(x,y)= 240.8928 corr(x,y)= cov(x,y)/sqrt(var(x)*var(y)= 240.8928/sqrt(1758.1664*261.5456)= 0.355239Related Questions
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