Question

A manufacturer of band saws wants to estimate the average repair cost per month for the saws he has sold to certain industries. He cannot obtain a repair cost for each saw, but he can obtain the total amount spent for saw repairs and the number of saws owned by each industry. Thus, he decides to use cluster sampling, with each industry as a cluster. The manufacturer selects a simple random sample of n = 20 from the N = 96 industries he services. The data on total cost of repairs per industry and number of saws per industry are as given in the accompanying table. Estimate the average repair cost per saw for the past month and place a bound on the error of estimation.

Industry No.of saws Total repair cost for past month
1 3 50
2 7 110
3 11 230
4 9 140
5 2 60
6 12 280
7 14 240
8 3 45
9 5 60
10 9 230
11 8 140
12 6 130
13 3 70
14 2 50
15 1 10
16 4 60
17 12 280
18 6 150
19 5 110
20 8 120

Answer 1

The average repair cost per saw for the past month is 20.

The bound of error of estimation is ±10.

Explanation:

a) Data and Calculations:

Industry No.of saws Total repair cost Average

for past month

1 3 50 16.67

2 7 110 15.71

3 11 230 20.91

4 9 140 15.56

5 2 60 30

6 12 280 23.33

7 14 240 17.14

8 3 45 15

9 5 60 12

10 9 230 25.56

11 8 140 17.50

12 6 130 21.67

13 3 70 23.33

14 2 50 25

15 1 10 10

16 4 60 15

17 12 280 23.33

18 6 150 25

19 5 110 22

20 8 120 15

Total 130 2,565 19.73

Average = Sum of the total repair cost for past month divided by the number of saws repaired

= 19.73 (2,565/130)

= 20

The bound on error of estimation = the difference between the upper bound of the interval and the calculated mean

= 30 - 20

= 10

The lower bound = 10

The bound of error is also = (30 -10)/2 = 10