Problem Sheet V ANOVA
PROBLEM SHEET – V
1. A sales manager has experience with four different sales approaches and has a large group of salesmen applying each of four approaches (A, B, C and D). He samples at random from each group, thus obtaining the data shown below in the table. Analyze this data using analysis of variance (0.05 level) in testing whether any real difference exists between the four sales approaches as they relate to the successful completion of sales.
Rupees of Sale Resulting from Application of Four Sales Approaches
Sales Approach A
B
C
D
12
11
16
14
10
13
14
15
13
12
10
9
11
8
7
9
17
12
14
13
10
Total 76
54
54
66
2. A marketing researcher wishes to test whether any significant difference exists between the performances of three retail stores in their sales of a particular product. Test whether the average of the retail store sales are equal at the 0.05 level. Tubular values represent in Rs. lakhs.
Retail Stores
I
II
III
12
14
6
12
13
16
15
17
19
13
12
10
9
14
13
3. Four different give-away premiums are being tried in a test area to determine if any significant difference exists in their ability to attract buying customers. Sales are recorded for the stores using each of the four premiums. Test at the 0.01 level. Tubular values represent sales in Rs. lakhs. Premium
I
II
III
IV
35
42
63
21
13
48
60
33
39
40
43
49
55
50
50
43
36
42
80
70
4. An investor has some money which he wants to invest in shares. Obviously, he would like to invest in those shares promise higher returns. Also, he doesn’t want to invest all his money in one; rather he wants to distribute it in three shares. He has collected the following information on five different shares in ten randomly selected time periods. Can you help the investor in deciding which three shares to invest his money in? (Note: The last two rows give the column sum and column SS respectively).
RATE OF RETURN IN
DCM
JK
LCP
ABC
XYZ
28.32
40.65
33.98
33.75
27.73
22.71
30.62
43.61
24.64
26.73
14.41
32.98
36.77
1. A sales manager has experience with four different sales approaches and has a large group of salesmen applying each of four approaches (A, B, C and D). He samples at random from each group, thus obtaining the data shown below in the table. Analyze this data using analysis of variance (0.05 level) in testing whether any real difference exists between the four sales approaches as they relate to the successful completion of sales.
Rupees of Sale Resulting from Application of Four Sales Approaches
Sales Approach A
B
C
D
12
11
16
14
10
13
14
15
13
12
10
9
11
8
7
9
17
12
14
13
10
Total 76
54
54
66
2. A marketing researcher wishes to test whether any significant difference exists between the performances of three retail stores in their sales of a particular product. Test whether the average of the retail store sales are equal at the 0.05 level. Tubular values represent in Rs. lakhs.
Retail Stores
I
II
III
12
14
6
12
13
16
15
17
19
13
12
10
9
14
13
3. Four different give-away premiums are being tried in a test area to determine if any significant difference exists in their ability to attract buying customers. Sales are recorded for the stores using each of the four premiums. Test at the 0.01 level. Tubular values represent sales in Rs. lakhs. Premium
I
II
III
IV
35
42
63
21
13
48
60
33
39
40
43
49
55
50
50
43
36
42
80
70
4. An investor has some money which he wants to invest in shares. Obviously, he would like to invest in those shares promise higher returns. Also, he doesn’t want to invest all his money in one; rather he wants to distribute it in three shares. He has collected the following information on five different shares in ten randomly selected time periods. Can you help the investor in deciding which three shares to invest his money in? (Note: The last two rows give the column sum and column SS respectively).
RATE OF RETURN IN
DCM
JK
LCP
ABC
XYZ
28.32
40.65
33.98
33.75
27.73
22.71
30.62
43.61
24.64
26.73
14.41
32.98
36.77