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A suburban hotel derives its gross income 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 Income Occupied Day Income Occupied 1 $1,452 23 14 $1425 272 1361 47 15 1445 343 1426 21 16 1439 154 1470 39 17 1348 195 1456 37 18 1450 386 1430 29 19 1431 447 1354 23 20 1446 478 1442 44 21 1485 439 1394 45 22 1405 3810 1459 16 23 1461 5111 1399 30 24 1490 6112 1458 42 25 1426 3913 1537 54
Use a statistical software package to answer the following questions.
a. Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.b. Determine the coefficient of correlation between the two variables. Interpret the value. c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?
Make the appropriate test statistics & the rejection of your test.
Find the cost of the shortest length of carpet.
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The Orthogonal group On is the set of all nxn matrices with entries in R such that AA^t = 1. The special orthogonal group SOn is the subset of all matrices in On with det(A) = 1.
A sample originally has a mass of 800 mg. Find a formula for the mass remaining after t days.
Sketch the sets of points determined by the following relations:
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