Signatures to a petition were collected on 676 sheets. Each sheet has enough space for 42 signatures, but on many sheets a smaller number of signatures was collected. The number of signatures per sheet were counted on a random sample of 50 sheets. The results are given below:
|
Number of signatures
|
42
|
41
|
36
|
32
|
29
|
27
|
23
|
19
|
16
|
15
|
|
Frequency
|
23
|
4
|
1
|
1
|
1
|
2
|
1
|
1
|
2
|
1
|
| |
|
|
|
|
|
|
|
|
|
|
|
Number of signatures
|
14
|
11
|
10
|
9
|
7
|
6
|
5
|
4
|
3
|
Total
|
|
Frequency
|
1
|
1
|
1
|
1
|
1
|
3
|
2
|
1
|
1
|
50
|
a) Give an 80% confidence interval for the total number of signatures.
b) How (if at all) does the non-normality of the Number of signatures (with a greatest frequency at the upper end - 42) affect your answer?
c). After the sample in the Table of question 1 was taken, the total number of completely filled sheets (with 42 signatures each) was counted and found to be 326 (out of the total of 676). Use this infornmation to improve your estimate of the total number of signatures and find a standard error to that estimate.