Question
Match the following steps (with the description) of finding x-limits for given probabilities of a normal distribution.
_____ A fundamental principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
_____ The distribution of a sample statistic obtained from multiple samples of the same size from a population.
_____ A measure of the variability of a sample statistic calculated as the standard deviation of the sampling distribution.
1. Sampling Distribution
2. Central Limit Theorem
3. Standard Error
_____ A fundamental principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
_____ The distribution of a sample statistic obtained from multiple samples of the same size from a population.
_____ A measure of the variability of a sample statistic calculated as the standard deviation of the sampling distribution.
1. Sampling Distribution
2. Central Limit Theorem
3. Standard Error
Answers
GPT-4o mini
Here are the correct matches for the steps and their descriptions:
- **2. Central Limit Theorem**: A fundamental principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
- **1. Sampling Distribution**: The distribution of a sample statistic obtained from multiple samples of the same size from a population.
- **3. Standard Error**: A measure of the variability of a sample statistic calculated as the standard deviation of the sampling distribution.
So the final matches are:
- Central Limit Theorem → 2
- Sampling Distribution → 1
- Standard Error → 3
- **2. Central Limit Theorem**: A fundamental principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
- **1. Sampling Distribution**: The distribution of a sample statistic obtained from multiple samples of the same size from a population.
- **3. Standard Error**: A measure of the variability of a sample statistic calculated as the standard deviation of the sampling distribution.
So the final matches are:
- Central Limit Theorem → 2
- Sampling Distribution → 1
- Standard Error → 3