Random Sample
Definition
A random sample is a subset of individuals selected from a larger population in such a way that every individual has an equal chance of being chosen. It helps to ensure that the sample is representative of the population.
Analogy
Imagine you have a jar filled with different colored candies. To get a random sample, you close your eyes and randomly pick a few candies from the jar without looking. This way, every candy has an equal chance of being chosen.
Related terms
Sampling Bias: Sampling bias occurs when certain individuals or groups are more likely to be included in a sample than others, leading to an unrepresentative sample.
Simple Random Sample: A simple random sample is a subset of individuals selected from a larger population where each possible sample has an equal probability of being chosen.
Stratified Sampling: Stratified sampling involves dividing the population into subgroups (strata) based on specific characteristics and then selecting samples from each stratum.
"Random Sample" appears in:
Subjects (1)
Study guides (11)
AP Statistics - 4.11 Parameters for a Binomial Distribution
AP Statistics - 6.1 Introducing Statistics: Why Be Normal?
AP Statistics - 6.2 Constructing a Confidence Interval for a Population Proportion
AP Statistics - 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion
AP Statistics - 6.10 Setting Up a Test for the Difference of Two Population Proportions
AP Statistics - 7.1 Introducing Statistics: Should I Worry About Error?
AP Statistics - 8.2 Setting Up a Chi Square Goodness of Fit Test
AP Statistics - 8.5 Setting Up a Chi-Square Test for Homogeneity or Independence
AP Statistics - 8.7 Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data
AP Statistics - 9.2 Confidence Intervals for the Slope of a Regression Model
AP Statistics - 9.4 Setting Up a Test for the Slope of a Regression Model
Additional resources (1)
Practice Questions (15)
- Suppose we conduct a chi-square goodness of fit test to examine the distribution of eye colors in a population. We collect data from a random sample of 500 individuals and obtain the following observed frequencies: 100 with brown eyes, 200 with blue eyes, 120 with green eyes, and 80 with hazel eyes. The expected proportions are 40%, 15%, 20%, and 25%, respectively. To calculate the test statistic for this scenario, what would be the next step?
- A marketing researcher wants to estimate the proportion of adults who own smartphones. He collects data from a random sample of 500 adults and finds that 350 of them own smartphones. Which of the following procedures should he use?
- A biologist wants to determine if the average lifespan of a certain species of bird is less than 5 years. They collect data from a random sample of 50 birds and calculate the sample mean lifespan to be 4.8 years and the sample standard deviation to be 0.3 years. Which of the following procedures should they use?
- A researcher wants to investigate if there is a relationship between the height and weight of individuals or not. They collect data from a random sample of 100 individuals. Which of the following procedures is the most appropriate to use?
- A psychologist wants to investigate if there is a significant difference in anxiety levels before and after a treatment. He collects data from a random sample of 50 individuals and wants to conduct a hypothesis test. Which of the following procedures is most appropriate for him to use?
- A researcher wants to investigate if the distribution of car colors in a city is different from the expected distribution. They collect the color values of a random sample of 500 cars. Which of the following procedures should be used?
- A researcher wants to estimate the proportion of college students who own a laptop. They survey a random sample of 1000 college students and find that 700 of them own laptops. Which of the following procedures is most appropriate?
- A researcher wants to investigate if there is a significant association between favorite type of music (rock, pop, jazz) and age group (teenagers, young adults, middle-aged adults). They collect data from a random sample of 200 individuals and create a contingency table. Which of the following procedures is most appropriate?
- A researcher wants to estimate the mean weight of a certain breed of dogs. He collects data from a random sample of 50 dogs and calculates the sample mean weight to be 25 pounds. Which of the following procedures should he use?
- A researcher wants to investigate if the distribution of the level of education (high school, college, graduate) within different income level groups (low, medium, high) are the same. She collects data from a random sample of 500 individuals and creates a contingency table. Which of the following procedures is most appropriate for her to use?
- What is the main purpose of using a confidence interval based on a random sample to test a claimed population proportion?
- What is the purpose of testing a claimed population proportion using a confidence interval based on a random sample?
- An university states that 92% of all 20,000 of its students know who Taylor Swift is. To test this claim, a club polls a random sample of 1313 students at the university and finds that 998 of them know of her. Is the Independent condition for the one-proportion z-test satisfied?
- If we do not have a random sample in a one-proportion z-test, can we infer anything about the population?
- An online survey claims that 80% of adults support the use of renewable energy sources. To test this claim, a random sample of 500 adults is selected, and it is found that 390 of them support the use of renewable energy sources. What are the appropriate hypotheses for conducting a one-proportion z-test to test this claim?
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