Practice Population vs Sample in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

In statistics, the population is the entire group of individuals or items you want to study, while the sample is the smaller subset you actually collect data from. We use sample statistics to estimate unknown population parameters.

You want to know the average height of ALL teenagers in your country (population), but you can't measure everyone. So you measure 1000 teenagers (sample) and use that to estimate the whole.

Showing a random 20 of 76 problems.

Example 1

easy
True or false: in most studies we can measure the entire population directly.

Example 2

challenge
A researcher samples 500 from a population and computes a mean of 50. She then realizes 100 of those 500 were accidentally measured twice (so really only 400 distinct people, 100 counted twice). Does the duplication change which group is the population? What is the true sample size of distinct individuals?

Example 3

easy
In the same study, what is the sample?

Example 4

medium
Distinguish between a parameter and a statistic. Give an example of each.

Example 5

easy
Which of these is a parameter: the average height of all 10001000 students in a school, or the average height of 5050 surveyed students?

Example 6

hard
Match: ฮผ,ฯƒ,p,xห‰,s,p^\mu, \sigma, p, \bar{x}, s, \hat{p} โ€” which three are parameters?

Example 7

medium
Two studies estimate the same population mean: study A samples 100, study B samples 2,500 (both random). Which sample mean is expected to be closer to the true mean, and why?

Example 8

medium
A population has true mean ฮผ=72\mu = 72. Two random samples of size n=30n = 30 give sample means xห‰1=70.5\bar{x}_1 = 70.5 and xห‰2=73.8\bar{x}_2 = 73.8. What is the name for the natural difference between samples?

Example 9

medium
A city has 2,0002{,}000 small businesses. A researcher contacts every single one of them and records revenue. What kind of study is this?

Example 10

easy
A company has 80008000 customers. A satisfaction survey reaches 600600 of them. Identify the sampling fraction.

Example 11

hard
Two factories make light bulbs. Factory A has a sample mean lifetime xห‰A=990\bar{x}_A = 990 hr from n=100n=100. Factory B has xห‰B=1010\bar{x}_B = 1010 hr from n=20n=20. Can we be confident Factory B's bulbs last longer on average? Explain briefly.

Example 12

medium
A study reports: 'Among the 250250 patients in our trial, average blood pressure dropped 88 mmHg.' Identify (a) the population, (b) the sample, (c) the statistic.

Example 13

medium
Fill in the blank: 'A ____ is to a sample as a parameter is to a population.'

Example 14

challenge
To estimate the mean of a population of 10,000, a researcher can either census all 10,000 or randomly sample 1,000. The census has data-entry errors on 5% of records; the random sample is entered carefully with no errors. Argue which may give a more accurate estimate of the true mean.

Example 15

easy
A biologist wants to estimate the average weight of all salmon in a river. She catches 8080 salmon and weighs them. Identify the sample size nn.

Example 16

medium
A teacher claims her 30-student class average of 85 proves 'all students in the school average 85.' Identify the population, the sample, and the flaw.

Example 17

medium
An online news site polls its own readers about national policy. What is the population the poll can credibly describe, and what is the population the headline likely claims?

Example 18

medium
In a quality check, 30 of 6,000 light bulbs are tested and 2 are defective. Estimate the population defect rate and state whether it is a statistic or parameter.

Example 19

easy
A number that describes a population is called a ____.

Example 20

easy
A company has 5,000 employees. HR surveys 250. Which number is the sample size?
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