Representatives of hotels, restaurants, hotel and restaurant supply companies, and other businesses located in Portland, Oregon, organized an association to attract conventions to their city. Members were asked to make contributions equal to 1 percent of their sales to finance the association. To aid collections, hotel members, including Hilton Hotels Corporation, agreed to give preferential treatment to suppliers who paid their assessments and to curtail purchases from those who did not. This agreement violated federal antitrust laws. The United States sued the members of the association, including Hilton Hotels, for the crime of violating federal antitrust laws. Can a corporation be held criminally liable for the acts of its representatives? If so, what criminal penalties can be assessed against the corporation? United States v. Hilton Hotels Corp., 467 F.2d 1000, Web 1972 U.S. App. Lexis 7414 (United States Court of Appeals for the Ninth Circuit)

Forecasting labour costs is a key aspect of hotel revenue management that enables hoteliers to appropriately allocate hotel resources and fix pricing strategies. Mary, the President of Hellenic Hoteliers Federation (HHF) is interested in investigating how labour costs (variable L_COST) relate to the number of rooms in a hotel (variable Total_Rooms). Suppose that HHF has hired you as a business analyst to develop a linear model to predict hotel labour costs based on the total number of rooms per hotel using the data provided.

3.1 Use the least squares method to estimate the regression coefficients b0 and b1

3.2 State the regression equation

3.3 Plot on the same graph, the scatter diagram and the regression line

3.4 Give the interpretation of the regression coefficients b0 and b1 as well as the result of the t-test on the individual variables (assume a significance level of 5%)

3.5 Determine the correlation coefficient of the two variables and provide an interpretation of its meaning in the context of this problem 3.6 Check statistically, at the 0.05 level of significance whether there is any evidence of a linear relationship between labour cost and total number of rooms per hotel

I need only the 3.4 and 3.5 questions.

Total_Rooms   L_COST
412   2.165.000
313   2.214.985
265   1.393.550
204   2.460.634
172   1.151.600
133   801.469
127   1.072.000
322   1.608.013
241   793.009
172   1.383.854
121   494.566
70   437.684
65   83.000
93   626.000
75   37.735
69   256.658
66   230.000
54   200.000
68   199.000
57   11.720
38   59.200
27   130.000
47   255.020
32   3.500
27   20.906
48   284.569
39   107.447
35   64.702
23   6.500
25   156.316
10   15.950
18   722.069
17   6.121
29   30.000
21   5.700
23   50.237
15   19.670
8   7.888
20  
11  
15   3.500
18   112.181
23  
10   30.000
26   3.575
306   2.074.000
240   1.312.601
330   434.237
139   495.000
353   1.511.457
324   1.800.000
276   2.050.000
221   623.117
200   796.026
117   360.000
170   538.848
122   568.536
57   300.000
62   249.205
98   150.000
75   220.000
62   50.302
50   517.729
27   51.000
44   75.704
33   271.724
25   118.049
42  
30   40.000
44  
10   10.000
18   10.000
18  
73   70.000
21   12.000
22   20.000
25   36.277
25   36.277
31   10.450
16   14.300
15   4.296
12  
11  
16   379.498
22   1.520
12   45.000
34   96.619
37   270.000
25   60.000
10   12.500
270   1.934.820
261   3.000.000
219   1.675.995
280   903.000
378   2.429.367
181   1.143.850
166   900.000
119   600.000
174   2.500.000
124   1.103.939
112   363.825
227   1.538.000
161   1.370.968
216   1.339.903
102   173.481
96   210.000
97   441.737
56   96.000
72   177.833
62   252.390
78   377.182
74   111.000
33   238.000
30   45.000
39   50.000
32   40.000
25   61.766
41   166.903
24   116.056
49   41.000
43   195.821
9  
20   96.713
32   6.500
14   5.500
14   4.000
13   15.000
13   9.500
53   48.200
11   3.000
16   27.084
21   30.000
21   20.000
46   43.549
21   10.000

Forecasting labour costs is a key aspect of hotel revenue management that enables hoteliers to appropriately allocate hotel resources and fix pricing strategies. Mary, the President of Hellenic Hoteliers Federation (HHF) is interested in investigating how labour costs (variable L_COST) relate to the number of rooms in a hotel (variable Total_Rooms). Suppose that HHF has hired you as a business analyst to develop a linear model to predict hotel labour costs based on the total number of rooms per hotel using the data provided.

3.1 Use the least squares method to estimate the regression coefficients b0 and b1

3.2 State the regression equation

3.3 Plot on the same graph, the scatter diagram and the regression line

3.4 Give the interpretation of the regression coefficients b0 and b1 as well as the result of the t-test on the individual variables (assume a significance level of 5%)

3.5 Determine the correlation coefficient of the two variables and provide an interpretation of its meaning in the context of this problem 3.6 Check statistically, at the 0.05 level of significance whether there is any evidence of a linear relationship between labour cost and total number of rooms per hotel

Total_Rooms   L_COST
412   2.165.000
313   2.214.985
265   1.393.550
204   2.460.634
172   1.151.600
133   801.469
127   1.072.000
322   1.608.013
241   793.009
172   1.383.854
121   494.566
70   437.684
65   83.000
93   626.000
75   37.735
69   256.658
66   230.000
54   200.000
68   199.000
57   11.720
38   59.200
27   130.000
47   255.020
32   3.500
27   20.906
48   284.569
39   107.447
35   64.702
23   6.500
25   156.316
10   15.950
18   722.069
17   6.121
29   30.000
21   5.700
23   50.237
15   19.670
8   7.888
20  
11  
15   3.500
18   112.181
23  
10   30.000
26   3.575
306   2.074.000
240   1.312.601
330   434.237
139   495.000
353   1.511.457
324   1.800.000
276   2.050.000
221   623.117
200   796.026
117   360.000
170   538.848
122   568.536
57   300.000
62   249.205
98   150.000
75   220.000
62   50.302
50   517.729
27   51.000
44   75.704
33   271.724
25   118.049
42  
30   40.000
44  
10   10.000
18   10.000
18  
73   70.000
21   12.000
22   20.000
25   36.277
25   36.277
31   10.450
16   14.300
15   4.296
12  
11  
16   379.498
22   1.520
12   45.000
34   96.619
37   270.000
25   60.000
10   12.500
270   1.934.820
261   3.000.000
219   1.675.995
280   903.000
378   2.429.367
181   1.143.850
166   900.000
119   600.000
174   2.500.000
124   1.103.939
112   363.825
227   1.538.000
161   1.370.968
216   1.339.903
102   173.481
96   210.000
97   441.737
56   96.000
72   177.833
62   252.390
78   377.182
74   111.000
33   238.000
30   45.000
39   50.000
32   40.000
25   61.766
41   166.903
24   116.056
49   41.000
43   195.821
9  
20   96.713
32   6.500
14   5.500
14   4.000
13   15.000
13   9.500
53   48.200
11   3.000
16   27.084
21   30.000
21   20.000
46   43.549
21   10.000

Consider eruptions of Old Faithful geyser in Yellowstone National Park. The distribution of eruptions is said to be roughly normal and based on a study done in the park in 2011 has a mean time between eruptions of 93 minutes with a standard deviation of 9.5 minutes.

A)Suppose we are still studying 60 eruptions and we want to know what the longest 5% of mean times between eruptions would be. What average time would put us in the longest 5%?

B)How would your previous answer change if we were only studying 20 eruptions?

C)If we study 45 eruptions, what is the chance that a mean eruption time would differ from the true mean by less than 5 minutes?

D)If we study 45 eruptions, what is the chance that a mean eruption time would differ from the true mean by less than 1 minute?

1. Fossa (a terrestrial mammal in Madagascar) experience a population decline of 20% each time a cyclone hit a particular national park on the African coast, because their prey populations also decline rapidly. Usually, one cyclone hits every 10 years. However, in one unusual year, five cyclones hit this national park and the population was reduced in quick succession to a level that was then easily wiped out by hunters. The primary causes of this population’s extinction were:

a) Over-Exploitation & Demographic Stochasticity

b) Over-Exploitation & Environmental Stochasticity

c) Demographic Stochasticity & Habitat Loss

d) Environmental Stochasticity & Habitat Loss

e) Demographic & Environmental Stochasticity

2. For a decreasing population, which of the following could be true regarding a declining population?

A survey found that​ women's heights are normally distributed with mean

62.1

in. and standard deviation

3.1 in. The survey also found that​ men's heights are normally distributed with mean 69.6 in. and standard deviation 3.7

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

56 in. and a maximum of

63in. Complete parts​ (a) and​ (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

The percentage of men who meet the height requirement is

nothing​%.

​(Round to two decimal places as​ needed.)

Since most men

▼

meet

do not meet

the height​ requirement, it is likely that most of the characters are

▼

women.

men.

b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements?

The new height requirements are a minimum of nothing in. and a maximum of nothing in.

1.

A random sample of ten households in College Park revealed they generated a mean of 10.91 pounds of garbage per week with a standard deviation of 4.736 pounds. Construct the 80% confidence interval to estimate the mean amount of garbage all College Park households generate per week

8.1646 pounds to 13.6554 pounds

7.5220 pounds to 14.2980 pounds

8.8387 pounds to 12.9813 pounds

6.0429 pounds to 15.7771 pounds

2.

Suppose National Collegiate Athletic Association [NCAA] rules state all student-athletes are to receive an average of 50 hours of academic support, per term. A random sample of 49 University of Maryland student-athletes revealed a mean of 47.5 hours of academic support per term. If the calculated value for the associated test statistic equaled -1.75, what was the standard deviation of the number of hours of academic support the student-athletes in the sample received per term?

12

15

7

10

Taking the family to an amusement park has become increasingly costly according to the industry publication Amusement Business, which provides figures on the cost for a family of four to spend the day at one of America’s amusement parks. A random sample of 25 families of four that attended amusement parks yielded the following costs, rounded to the nearest dollar.

Given the cost is normally distributed.

a) Suppose the population standard deviation is $21. Determine a 95% confidence interval for the mean cost of a family of four to spend the day at an American amusement park.

c) What is the margin of error of the 95% confidence interval obtained ?

d) Suppose we want to find a 95% confidence interval with margin of error 0.5. How many samples shall we collect?