In: Economics
Sales Data provides data on a sample of customers. An industry trade publication stated that the average profit per customer for this industry was at least $4,500. Using a test of hypothesis, do the data support this claim or not?
Customer | Percent Gross Profit | Gross Sales | Gross Profit | Industry Code | Competitive Rating* |
1 | 51.0% | $170.00 | $86.70 | 1 | 2 |
2 | 32.0% | $181.00 | $57.92 | 3 | 4 |
3 | 20.0% | $203.00 | $40.60 | 2 | 2 |
4 | 22.0% | $249.00 | $54.78 | 5 | 1 |
5 | 21.0% | $476.00 | $99.96 | 5 | 1 |
6 | 21.0% | $476.00 | $99.96 | 5 | 4 |
7 | 22.0% | $635.00 | $139.70 | 2 | 3 |
8 | 34.0% | $856.00 | $291.04 | 3 | 3 |
9 | 26.0% | $1,062.00 | $276.12 | 4 | 2 |
10 | 16.6% | $1,110.00 | $183.71 | 7 | 3 |
11 | 20.0% | $1,153.00 | $230.60 | 7 | 3 |
12 | 36.0% | $1,392.00 | $501.12 | 4 | 2 |
13 | 18.0% | $1,743.00 | $313.74 | 4 | 2 |
14 | 20.0% | $2,307.00 | $461.40 | 7 | 3 |
15 | 5.0% | $2,534.00 | $126.70 | 4 | 5 |
16 | 29.0% | $2,683.00 | $778.07 | 7 | 2 |
17 | 10.0% | $2,780.00 | $278.00 | 2 | 3 |
18 | 37.0% | $3,272.00 | $1,210.64 | 5 | 3 |
19 | 60.0% | $3,864.00 | $2,318.40 | 7 | 1 |
20 | 24.0% | $3,988.00 | $957.12 | 6 | 3 |
21 | 9.0% | $4,072.00 | $366.48 | 7 | 3 |
22 | 50.0% | $4,190.00 | $2,095.00 | 5 | 3 |
23 | 17.0% | $4,219.00 | $717.23 | 3 | 4 |
24 | 32.0% | $4,711.00 | $1,507.52 | 7 | 1 |
25 | 15.0% | $4,824.00 | $723.60 | 6 | 3 |
26 | 10.0% | $4,878.00 | $487.80 | 7 | 4 |
27 | 13.0% | $5,157.00 | $670.41 | 7 | 2 |
28 | 22.0% | $5,552.00 | $1,221.44 | 2 | 3 |
29 | 17.0% | $5,876.00 | $998.92 | 1 | 3 |
30 | 19.0% | $5,888.00 | $1,118.72 | 6 | 4 |
31 | 6.0% | $7,632.00 | $457.92 | 5 | 4 |
32 | 23.0% | $8,058.00 | $1,853.34 | 3 | 3 |
33 | 23.0% | $12,056.00 | $2,772.88 | 7 | 2 |
34 | 14.0% | $12,981.00 | $1,817.34 | 2 | 4 |
35 | 22.0% | $13,406.00 | $2,949.32 | 2 | 3 |
36 | 14.0% | $15,882.00 | $2,223.48 | 7 | 3 |
37 | 28.0% | $16,343.00 | $4,576.04 | 3 | 3 |
38 | 27.0% | $19,985.00 | $5,395.95 | 5 | 3 |
39 | 3.0% | $20,160.00 | $604.80 | 5 | 5 |
40 | 46.0% | $26,616.00 | $12,243.36 | 5 | 2 |
41 | 26.0% | $28,018.00 | $7,284.68 | 5 | 3 |
42 | 11.0% | $28,950.00 | $3,184.50 | 4 | 4 |
43 | 18.0% | $29,646.00 | $5,336.28 | 4 | 3 |
44 | 37.0% | $31,019.00 | $11,477.03 | 6 | 1 |
45 | 20.0% | $31,305.00 | $6,261.00 | 2 | 3 |
46 | 21.0% | $34,769.00 | $7,301.49 | 7 | 1 |
47 | 10.0% | $34,817.00 | $3,481.70 | 4 | 3 |
48 | 14.0% | $38,609.00 | $5,405.26 | 1 | 3 |
49 | 9.0% | $38,923.00 | $3,503.07 | 2 | 5 |
50 | 16.0% | $40,536.00 | $6,485.76 | 4 | 3 |
51 | 22.0% | $54,851.00 | $12,067.22 | 6 | 2 |
52 | 21.0% | $54,861.00 | $11,520.81 | 7 | 2 |
53 | 17.0% | $58,063.00 | $9,870.71 | 5 | 4 |
54 | 11.0% | $62,862.00 | $6,914.82 | 4 | 5 |
55 | 7.0% | $78,574.00 | $5,500.18 | 3 | 5 |
56 | 14.0% | $92,776.00 | $12,988.64 | 4 | 3 |
57 | 15.0% | $112,837.00 | $16,925.55 | 1 | 4 |
58 | 13.0% | $115,999.00 | $15,079.87 | 4 | 5 |
59 | 21.0% | $120,854.00 | $25,379.34 | 5 | 4 |
60 | 14.0% | $179,101.00 | $25,074.14 | 6 | 3 |
*Rates the amount of competition for sales of the products sold to these customers: 1 = very little competition to 5 = very competitive |
Gross Profits | ||||
1 | 86.70 | |||
2 | 57.92 | |||
3 | 40.60 | |||
4 | 54.78 | |||
5 | 99.96 | |||
6 | 99.96 | |||
7 | 139.70 | |||
8 | 291.04 | |||
9 | 276.12 | |||
10 | 183.71 | |||
11 | 230.60 | |||
12 | 501.12 | |||
13 | 313.74 | |||
14 | 461.4 | |||
15 | 126.7 | |||
16 | 778.07 | |||
17 | 278 | |||
18 | 1,210.64 | |||
19 | 2,318.40 | |||
20 | 957.12 | |||
21 | 366.48 | |||
22 | 2,095.00 | |||
23 | 717.23 | |||
24 | 1,507.52 | |||
25 | 723.6 | |||
26 | 487.8 | |||
27 | 670.41 | |||
28 | 1,221.44 | |||
29 | 998.92 | |||
30 | 1,118.72 | |||
31 | 457.92 | |||
32 | 1,853.34 | |||
33 | 2,772.88 | |||
34 | 1,817.34 | |||
35 | 2,949.32 | |||
36 | 2,223.48 | |||
37 | 4,576.04 | |||
38 | 5,395.95 | |||
39 | 604.80 | |||
40 | 12,243.36 | |||
41 | 7,284.68 | |||
42 | 3,184.50 | |||
43 | 5,336.28 | |||
44 | 11,477.03 | |||
45 | 6,261.00 | |||
46 | 7,301.49 | |||
47 | 3,481.70 | |||
48 | 5,405.26 | |||
49 | 3,503.07 | |||
50 | 6,485.76 | |||
51 | 12,067.22 | |||
52 | 11,520.81 | |||
53 | 9,870.71 | |||
54 | 6,914.82 | |||
55 |
|
|||
56 | 12,988.64 | |||
57 | 16,925.55 | |||
58 | 15,079.87 | |||
59 | 25,379.34 | |||
60 | 25,074.14 | |||
4239.16467 | Mean | |||
5811.7292 | Standard deviation |
The t-test statistic will be used as shown below:
We set,
H0: 4500
HA: 4500
tstatistic= x - [/ (S/n)]
tstatistic= 4239.16467 - [4500 / (5811.7292 / 60)]
tstatistic= - 0.3476
The critical value comes out to be 1.67
Thus, the null hypothesis is rejected.