Library Donation Box Samples - 3 Problems - book types, election prediction, fish counts

Sep 30, 2026

Practice set of three statistics inference problems using small samples. A librarian analyzes samples of fiction vs non-fiction books from a donation box and compares expected proportions. A teacher samples student votes from each class to predict which candidate will win and estimates relative vote totals. A fisherman samples counts of minnows, goldfish, and sunfish from multiple nets to discuss what can and cannot be inferred about fish types and quantities.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Problem 1: Library donation books

Problem 2: Class election vote prediction

Problem 3: Lake fish count inference

Solve each problem. 1) In a library there was a donation box for books. A librarian wanted to estimate how many fiction and how many non-fiction books were in the box so she pulled out a sample. The results are shown below: |
Sample \# |
1 |
2 |
3 |
4 |
5 |
6 |
7 | | --- | --- | --- | --- | --- | --- | --- | --- | |
Fiction | 22 | 21 | 20 | 21 | 23 | 20 | 22 | |
Non-Fiction | 30 | 31 | 30 | 29 | 28 | 30 | 28 | Based on the information presented can you infer anything about the types of books donated? Based on the information presented there will be 27% more Non-Fiction books donated. 2) During a class election a teacher wanted to predict who would win. To do this she took a sample of students from each class and asked who they would vote for. The results are shown below: |
Sample \# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
Candidate A | 59 | 61 | 61 | 62 | 59 | 62 | 61 | 59 | |
Candidate B | 51 | 54 | 52 | 52 | 51 | 51 | 52 | 50 | Based on the information presented can you infer anything about who will win the election? Based on the information presented Candidate A will have 14% more votes. 3) In a lake there are 3 types of fish: minnows, goldfish and sunfish. A fisherman wanted to estimate how many of each type there were. He scooped up several nets full and recorded his results (shown below) . |
Sample \# |
1 |
2 |
3 | |
4 |
5 |
6 |
7 |
8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
minnows | 2 | 1 | | 4 | 5 | 5 | 4 | 3 | 1 | |
goldfish | 2 | 5 | | 5 | 5 | 5 | 3 | 3 | 5 | |
sunfish | 3 | 3 | | 1 | 3 | 4 | 3 | 1 | 3 | Based on the information presented can you infer anything about the number of different types of fish in the lake? Based on the information presented and the small samples gathered it is impossible to make any meaningful assumptions. Solve each problem. 1) In a library there was a donation box for books. A librarian wanted to estimate how many fiction and how many non-fiction books were in the box so she pulled out a sample. The results are shown below: |
Sample \# |
1 |
2 |
3 |
4 |
5 |
6 |
7 | | --- | --- | --- | --- | --- | --- | --- | --- | |
Fiction | 22 | 21 | 20 | 21 | 23 | 20 | 22 | |
Non-Fiction | 30 | 31 | 30 | 29 | 28 | 30 | 28 | Based on the information presented can you infer anything about the types of books donated? Based on the information presented there will be 27% more Non-Fiction books donated. 2) During a class election a teacher wanted to predict who would win. To do this she took a sample of students from each class and asked who they would vote for. The results are shown below: |
Sample \# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
Candidate A | 59 | 61 | 61 | 62 | 59 | 62 | 61 | 59 | |
Candidate B | 51 | 54 | 52 | 52 | 51 | 51 | 52 | 50 | Based on the information presented can you infer anything about who will win the election? Based on the information presented Candidate A will have 14% more votes. 3) In a lake there are 3 types of fish: minnows, goldfish and sunfish. A fisherman wanted to estimate how many of each type there were. He scooped up several nets full and recorded his results (shown below) . |
Sample \# |
1 |
2 |
3 | |
4 |
5 |
6 |
7 |
8 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
minnows | 2 | 1 | | 4 | 5 | 5 | 4 | 3 | 1 | |
goldfish | 2 | 5 | | 5 | 5 | 5 | 3 | 3 | 5 | |
sunfish | 3 | 3 | | 1 | 3 | 4 | 3 | 1 | 3 | Based on the information presented can you infer anything about the number of different types of fish in the lake? Based on the information presented and the small samples gathered it is impossible to make an

FAQs

What does Problem 1 ask you to infer from the fiction and non-fiction samples?

It asks whether anything can be inferred about the types of books donated and the relative amount of non-fiction compared with fiction.

What does Problem 2 ask you to infer about the class election?

It asks whether the sample voting results allow you to predict who will win and how the candidates’ totals compare.

What does Problem 3 ask you to infer about the fish in the lake?

It asks whether the sample net results support meaningful assumptions about the number of different fish types in the lake.

Sep 30, 2026

Uploaded by Alexandar