hi, i am trying to solve this problem but could not find the solution . please a
ID: 3232741 • Letter: H
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hi, i am trying to solve this problem but could not find the solution . please anyone help?
Case Study: Business Size The numbers of employees at businesses can vary. A business can have anywhere from a single employee to more than 1000 employees. The data shown below are the numbers of manufacturing businesses for several states in a recent year. (Source: U.S. Census Bureau) State Number of manufacturing businesses California 38,937 Illinois 14,210 Indiana 8,222 Michigan 12,378 New York 16,933 Ohio 14,729 Pennsylvania 14,167 Texas 19,593 Wisconsin 9,033 Number of Manufacturing Businesses Separated by Number of Employees State 1–4 5–9 10–19 20–49 50–99 100–249 250–499 500+ California 15,788 7,018 6,069 5,532 2,332 1,570 407 221 Illinois 4,989 2,364 2,328 2,219 1,146 831 213 120 Indiana 2,447 1,376 1,360 1,378 753 598 184 126 Michigan 4,485 2,143 2,013 1,910 872 676 184 95 New York 7,581 2,970 2,421 2,219 872 591 190 89 Ohio 4,700 2,582 2,502 2,442 1,188 911 262 142 Pennsylvania 4,670 2,476 2,359 2,364 1,088 854 235 121 Texas 7,352 3,396 3,099 2,922 1,362 973 303 186 Wisconsin 2,806 1,447 1,499 1,480 841 638 208 114 EXERCISES 1.) Employees: Which state has the greatest number of manufacturing employees? Explain your reasoning. 2.) Mean Business Size: Estimate the mean number of employees at a manufacturing business for each state. Use 1000 as the midpoint for “500+.” 3.) Employees: Which state has the greatest number of employees per manufacturing business? Explain your reasoning. 4.) Standard Deviation: Estimate the standard deviation for the number of employees at a manufacturing business for each state. Use 1000 as the midpoint for “500+.” 5.) Standard Deviation: Which state has the greatest standard deviation? Explain your reasoning. 6.) Distribution: Describe the distribution of the number of employees at manufacturing businesses for each state. Real Statistics — Real Decisions Putting it all together You are a member of your local apartment association. The association represents rental housing owners and managers who operate residential rental property throughout the greater metropolitan area. Recently, the association has received several complaints from tenants in a particular area of the city who feel that their monthly rental fees are much higher compared to other parts of the city. You want to investigate the rental fees. You gather the data shown in the table below. Area A represents the area of the city where tenants are unhappy about their monthly rents. The data represent the monthly rents paid by a random sample of tenants in Area A and three other areas of similar size. Assume all the apartments represented are approximately the same size with the same amenities. The Monthly Rents (in dollars) Paid by 12 Randomly Selected Apartment Tenants in 4 Areas of Your City Area A Area B Area C Area D 1275 1124 1085 928 1110 954 827 1096 975 815 793 862 862 1078 1170 735 1040 843 919 798 997 745 943 812 1119 796 756 1232 908 816 765 1036 890 938 809 998 1055 1082 1020 914 860 750 710 1005 975 703 775 930 EXERCISES 1.) How Would You Do It? (a) How would you investigate the complaints from renters who are unhappy about their monthly rents? (b) Which statistical measure do you think would best represent the data sets for the four areas of the city? (c) Calculate the measure from part (b) for each of the four areas. 2.) Displaying the Data (a) What type of graph would you choose to display the data? Explain your reasoning. (b) Construct the graph from part (a). (c) Based on your data displays, does it appear that the monthly rents in Area A are higher than the rents in the other areas of the city? Explain. 3.) Measuring the Data (a) What other statistical measures in this chapter could you use to analyze the monthly rent data? (b) Calculate the measures from part (a). (c) Compare the measures from part (b) with the graph you constructed in Exercise 2. Do the measurements support your conclusion in Exercise 2? Explain. 4.) Discussing the Data (a) Do you think the complaints in Area A are legitimate? How do you think they should be addressed? (b) What reasons might you give as to why the rents vary among different areas of the city? Highest Monthly Rents (median per city) San Jose, CA $1340 Thousand Oaks, CA $1301 Honolulu, HI $1237 San Francisco, CA $1224 Washington, D.C. $1190
Explanation / Answer
1.) Employees: Which state has the greatest number of manufacturing employees? Explain your reasoning.
Midpoint of the interval of Number of Employees State wise 1–4 5–9 10–19 20–49 50–99 100–249 250–499 500+
is (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000)
Number of employees in California = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (15788,7018,6069,5532,2332,1570,407,221)
= 1188571
Number of employees in Indiana = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (2447,1376,1360,1378,753,598,184,126)
= 438368
Number of employees in Illinois = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4989,2364,2328,2219,1146,831,213,120)
= 569487
Number of employees in Michigan = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4485,2143,2013,1910,872,676,184,95)
= 468131
Number of employees in NewYork = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (7581,2970,2421,2219,872,591,190,89)
= 479651
Number of employees in Ohio = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4700,2582,2502,2442,1188,911,262,142)
= 637946.5
Number of employees in Pennsylvania = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4670,2476,2359,2364,1088,854,235,121)
= 583857
Number of employees in Texas = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4670,2476,2359,2364,1088,854,235,121)
= 758627.5
Number of employees in Wisconsin = Sum of product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
= sum of (2.5 ,7.0, 14.5, 34.5, 74.5, 174.5, 374.5, 1000) * (4670,2476,2359,2364,1088,854,235,121)
= 455821
So, the the greatest number of manufacturing employees is in California (1188571).
2.) Mean Business Size: Estimate the mean number of employees at a manufacturing business for each state.
Mean number of employees at a manufacturing business = Total Employees / Total Manufacturing Businesses
Mean number of employees at a manufacturing business in California = 1188571 / 38937 = 30.52
Mean number of employees at a manufacturing business in Illinois = 569487/14210 = 40.08
Mean number of employees at a manufacturing business in Indiana = 438368/8222 = 53.32
Mean number of employees at a manufacturing business in Michigan = 468131/12378 = 37.82
Mean number of employees at a manufacturing business in NewYork = 479651/16933 = 28.33
Mean number of employees at a manufacturing business in Ohio = 637946.5/ 14729 = 43.31
Mean number of employees at a manufacturing business in Pennsylvania = 583857/14167 = 41.21
Mean number of employees at a manufacturing business in Texas = 758627.5/19593 = 38.72
Mean number of employees at a manufacturing business in Wisconsin = 455821/9033 = 50.46
3.) Employees: Which state has the greatest number of employees per manufacturing business? Explain your reasoning.
Highest mean number of employees at a manufacturing business is in Indiana ( 53.32), so Indiana has the greatest number of employees per manufacturing business.
4.) Standard Deviation: Estimate the standard deviation for the number of employees at a manufacturing business for each state
The number of employees in a state is the product of midpoints and Number of Manufacturing Businesses Separated by Number of Employees
Number of employees in California = (39470.0 49126.0 88000.5 190854.0 173734.0 273965.0 152421.5 221000.0)
The standard deviation of the above data is 83552.03
Number of employees in Illinois = (12472.5 16548.0 33756.0 76555.5 85377.0 145009.5 79768.5 120000.0)
The standard deviation of the above data is 47764.57
Number of employees in Indiana = (6117.5 9632.0 19720.0 47541.0 56098.5 104351.0 68908.0 126000.0)
The standard deviation of the above data is 43783.39
Number of employees in Michigan = (11212.5 15001.0 29188.5 65895.0 64964.0 117962.0 68908.0 95000.0)
The standard deviation of the above data is 37910.06
Number of employees in NewYork = (18952.5 20790.0 35104.5 76555.5 64964.0 103129.5 71155.0 89000.0)
The standard deviation of the above data is 31546.8
Number of employees in Ohio = (11750.0 18074.0 36279.0 84249.0 88506.0 158969.5 98119.0 142000.0)
The standard deviation of the above data is 54645.32
Number of employees in Pennsylvania = (11675.0 17332.0 34205.5 81558.0 81056.0 149023.0 88007.5 121000.0)
The standard deviation of the above data is 49006.64
Number of employees in Texas = (18380.0 23772.0 44935.5 100809.0 101469.0 169788.5 113473.5 186000.0)
The standard deviation of the above data is 62952.88
Number of employees in Wisconsin = (7015.0 10129.0 21735.5 51060.0 62654.5 111331.0 77896.0 114000.0)
The standard deviation of the above data is 42499.96
5.) Standard Deviation: Which state has the greatest standard deviation? Explain your reasoning
California has the greatest standard deviation (83552.03).
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