While what you describe involves a comparison, it would not involve two samples of at least 30 observations. There is data on all cars by category. I think if you choose the category with the most types of cars in it you could do a study like the averag

While what you describe involves a comparison, it would not involve two samples of at least 30 observations. There is data on all cars by category. I think if you choose the category with the most types of cars in it you could do a study like the averag. this is example

Do Apparel Stores Have a Higher Return on Equity (ROE) than Department Stores?

 

 

My population is the return on equity in all years for all apparel stores and return on equity in all years for all department stores.  The parameters are the mean return on equity for all apparel stores and the mean return on equity for all department stores.  The samples are 51 apparel stores and 30 department stores from Yahoo Finance on November 6, 2013.  I eliminated stores for which Yahoo did not have a ROE or that had negative ROE.  The statistics are the mean return on equity for 51 apparel stores which was 19.30and the mean return on equity for 30 department stores which was 16.47%.

 

Presentation of the data:

  

Department Store

ROE %

 

 

 

 

 

cumulative  

  lower

 

upper

midpoint

width

 frequency

percent 

   frequency

percent  

0.00

5.00

2.50

5.00

5  

16.7  

5  

16.7    

5.00

10.00

7.50

5.00

4  

13.3  

9  

30.0    

10.00

15.00

12.50

5.00

7  

23.3  

16  

53.3    

15.00

20.00

17.50

5.00

7  

23.3  

23  

76.7    

20.00

25.00

22.50

5.00

3  

10.0  

26  

86.7    

25.00

30.00

27.50

5.00

1  

3.3  

27  

90.0    

30.00

35.00

32.50

5.00

0  

0.0  

27  

90.0    

35.00

40.00

37.50

5.00

0  

0.0  

27  

90.0    

40.00

45.00

42.50

5.00

1  

3.3  

28  

93.3    

45.00

50.00

47.50

5.00

1  

3.3  

29  

96.7    

50.00

55.00

52.50

5.00

0  

0.0  

29  

96.7    

55.00

60.00

57.50

5.00

1  

3.3  

30  

100.0                   

30  

100.0     

 

 

 

 

 

Department Store      

 

ROE %  

count

30  

mean

16.41727  

sample standard deviation

12.64181  

sample variance

159.81544  

minimum

0.599  

maximum

55.215  

range

54.616     

  

Apparel stores

ROE %

 

 

 

 

 

cumulative  

  lower

 

upper

midpoint

width

 frequency

percent 

   frequency

percent  

0.00

10.00

5.00

10.00

12  

23.5  

12  

23.5    

10.00

20.00

15.00

10.00

22  

43.1  

34  

66.7    

20.00

30.00

25.00

10.00

8  

15.7  

42  

82.4    

30.00

40.00

35.00

10.00

3  

5.9  

45  

88.2    

40.00

50.00

45.00

10.00

4  

7.8  

49  

96.1    

50.00

60.00

55.00

10.00

1  

2.0  

50  

98.0    

60.00

70.00

65.00

10.00

0  

0.0  

50  

98.0    

70.00

80.00

75.00

10.00

1  

2.0  

51  

100.0                   

51  

100.0     

 

                                  

Apparel stores    

 

ROE %

count

51

mean

19.29759

sample standard deviation

14.90353

sample variance

222.11522

minimum

1.057

maximum

71.474

range

70.417

 

 

Hypothesis test:

Ho:  µAp  ≥ µDept   or  µAp – µDept  ≥  0

HA:  µAp  < µDept or µAp – µDept  <  0

Tcrit   = 2.462 ( using α = 0.01 in one tail and df = n – 1 = 30 – 1 =29 using the smaller of the sample sizes) In Excel, t.inv(.99,29)

Fail to reject Ho.  The 2.88% difference between the mean return on equity for apparel companies and the mean return on equity of department stores is not sufficient evidence to prove that the apparel companies have a significantly higher return on equity than department stores, on average.  There was quite a bit of variation within the two data sets which resulted in me not being confident in the difference I found between the two means.  Note that both had distributions that are skewed to the right, but since the sample sizes both exceed 30, I was able to use the normal distribution in the analysis.

 

 

Appendix:  Data table:

Department Stores  

Apparel Stores  

ROE %  

ROE %

Kirkcaldie & Stains Limited

0.599 

Ocean Sky International Ltd.

1.057

Bon-Ton Stores Inc.

0.616 

Destination XL Group, Inc.

1.273

Grupo Elektra, S.A. de C.V.

1.769 

Reitmans (Canada) Limited

1.437

Saks Incorporated

3.768 

Reitmans (Canada) Limited

1.437

Metro Holdings Limited

4.656 

LeRoi Holdings Ltd.

2.658

Sears Hometown and Outlet Stor

7.496 

Etam Developpement SA

4.509

Grupo Famsa SAB de CV

7.931 

New York & Company Inc.

5.409

Lianhua Supermarket

8.176 

Stage Stores Inc.

6.578

Organizacion Soriana

8.846 

Moss Bros Group PLC

6.944

New World Depa.Store Chin

10.184 

The Children

8.954

Sears Canada Inc.

11.801 

Joyce Boutique Holdings Ltd.

9.081

Parkson Retail Group Ltd.

11.987 

Jos. A Bank Clothiers Inc.

9.744

David Jones Limited

12.073 

Shoe Carnival Inc.

10.13

Wing On Company Inter

14.091 

Evergreen International

10.507

Century Ginwa Retail

14.306 

Ascena Retail Group Inc.

10.713

Intime Department Store Group

14.585 

Stein Mart Inc.

11.616

Springland International

15.368 

The Men’s Wearhouse, Inc.

11.701

Kohl’s Corp.

15.848 

I.T Ltd.

12.178

Services

16.887 

Trinity Ltd.

12.875

Marks & Spencer Group PLC

17.397 

Genesco Inc.

13.012

Dillard’s Inc.

18.037 

Premier Investments Limited

13.683

Debenhams PLC

18.201 

Abercrombie & Fitch Co.

14.525

Patagonia

19.034 

The Cato Corporation

14.8

Macy’s, Inc.

23.354 

Luxottica Group S.p.A.

14.812

Lifestyle International

23.667 

Luxottica Group SpA

14.812

Ashley (Laura) Holdings PLC

24.18 

Goldlion Holdings Ltd.

15.036

Golden Eagle Retail Group Ltd.

25.666 

Guess’ Inc.

15.107

Warehouse Group Limited (The)

41.039 

Kathmandu Holdings Limited

15.396

China Seven Star Shopping Ltd.

45.741 

Chico’s FAS Inc.

15.435

The TJX Companies, Inc.

55.215 

DSW Inc.

15.884   

Xtep International

15.929   

American Eagle Outfitters, Inc

16.762   

OrotonGroup Limited

17.265   

Urban Outfitters Inc.

19.715   

Specialty Fashion

21.308   

Destination Maternity Corporat

21.362   

Marisa Lojas SA

22.836   

Casual Male Retail Group, Inc.

25.52   

ANN INC.

25.902   

Tilly’s, Inc.

25.966   

Hallenstein Glasson Limited

27.969   

Giordano International Ltd.

29.615   

Industria De Diseno Textil SA

30.974   

Express Inc.

36.534   

Nordstrom Inc.

39.255   

The Gap, Inc.

40.749   

The Buckle, Inc.

44.135   

Ross Stores Inc.

46.945   

Cherokee Inc.

47.444   

TJX Companies

55.215   

Francesca’s Holdings Corporati

71.474

 

 

 

While what you describe involves a comparison, it would not involve two samples of at least 30 observations. There is data on all cars by category. I think if you choose the category with the most types of cars in it you could do a study like the averag