Sampling – Exercise 5
1) The University of Mars is interested in the grade-point average of the graduating seniors. Let N=1000 be the number of the graduating seniors. We take a random sample of n=9 students. Let x denote their SAT scores and y denote the grade-point average of the graduating seniors. Assume that the average SAT for the entire population is 600.
|
Student # |
x |
y |
|
1 |
550 |
2.8 |
|
2 |
630 |
3.1 |
|
3 |
570 |
2.9 |
|
4 |
650 |
3.3 |
|
5 |
700 |
3.5 |
|
6 |
520 |
3.0 |
|
7 |
720 |
3.6 |
|
8 |
660 |
3.5 |
|
9 |
575 |
3.2 |
|
Total |
5575 |
28.9 |
a)
Obtain a ratio estimate of spent the average grade-point average of a
graduating senior at the University of Mars, and set up a 95% confidence
interval for that average grade-point average of a graduating senior.
2)
A fictitious survey of 10 households in a small village gave the
following data on the number of members, the number of children, the number of
cars and the number of bicycles in each household:
|
Members |
Children |
Cars |
Bicycles |
|
4 |
2 |
1 |
2 |
|
5 |
3 |
2 |
3 |
|
2 |
0 |
1 |
2 |
|
4 |
2 |
1 |
1 |
|
6 |
3 |
2 |
2 |
|
3 |
1 |
1 |
1 |
|
5 |
2 |
2 |
2 |
|
3 |
1 |
1 |
1 |
|
2 |
0 |
2 |
1 |
|
1 |
0 |
1 |
1 |
Assuming that the total population in the village consists of 25
households with 100 members, obtain ratio estimates and confidence intervals
for the total number of children, cars and bicycles.
3)
The Toyota Company in Georgetown, Kentucky, wants to estimate the ratio
of the number of man-hours lost due to sickness of its employees. It has N=7000
employees and takes a sample of n=10 employees and obtains the following data:
|
Employee |
Hours lost in previous year |
Hours lost in current year |
|
1 |
15 |
14 |
|
2 |
18 |
20 |
|
3 |
30 |
34 |
|
4 |
25 |
18 |
|
5 |
10 |
15 |
|
6 |
20 |
25 |
|
7 |
16 |
20 |
|
8 |
12 |
15 |
|
9 |
13 |
10 |
|
10 |
2 |
5 |
a)
Obtain an estimate of the desired ratio and set up a 95% confidence
interval for it.
b)
Assuming that in the previous year the company lost 120,000 man-hours,
obtain a 95% confidence interval for the number of man-hours which will be lost
this year.
c)
Compute again a 95% confidence interval for the number of man-hours which
will be lost this year, but this time assuming that the data from the previous
year were unavailable. Compare the result with that obtained in b).