Question

In: Economics

Sales Data provides data on a sample of customers. An industry trade publication stated that the...

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

Solutions

Expert Solution

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
5,500.18
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.

Rahul Sunny answered 2 years ago
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