Homework SourseA suburban hotel derives its gross income from its hotel and
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.
Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)
State the decision rule for 0.05 significance level: H0: ? ? 0; H1: ? > 0 (Round your answer to 3 decimal places.)
Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.05 significance level.
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. Omit the \"%\" sign in your response.)
| 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. |
Solution
MINITAB software used
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.)
Correlation: Income, Occupied
Pearson correlation of Income and Occupied = 0.405
Pearson correlation = 0.405
State the decision rule for 0.05 significance level: H0: ? ? 0; H1: ? > 0 (Round your answer to 3 decimal places.)
Reject Ho if t> 1.771 ( upper tail test with 13 DF)
Compute the value of the test statistic. (Round your answer to 2 decimal places.)
T= r/sqrt((1-r*r)/(n-2)) = 0.405/(sqrt(1-0.405*0.405)/(15-2)) = 1.60
Value of the test statistic = 1.60
(c)
Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.05 significance level.
Reject H0, There is a positive correlation between revenue and occupied rooms.
(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. Omit the \"%\" sign in your response.)
r*r= 0.405*0.405= 0.164025
% of the variation in revenue is explained by variation in occupied rooms = 16.4
