Which of the following criteria are necessary conditions for making a statistical inference? sample size greater than 30, or an approximately normal data set sample size greater than 100 convenience sample simple random sample systematic sample Dons

To make a statistical inference, certain criteria must be met to ensure the validity and reliability of the results. Let's analyze the given options: 1. **Sample size greater than 30**: This is a common rule of thumb in statistics, known as the "30-30-30 rule." It suggests that a sample size of at least 30 is generally sufficient for making inferences about a population. This is because with a sample size of 30, the Central Limit Theorem (CLT) starts to hold, and the sampling distribution of the sample mean will be approximately normal, even if the population distribution is not normal. 2. **Approximately normal data set**: This criterion is necessary for making inferences about the population mean using the sample mean. If the data set is not approximately normal, the sampling distribution of the sample mean will not be normal, and the standard error of the mean will not be a reliable estimate of the population standard deviation. 3. **Sample size greater than 100**: While a larger sample size is generally better for making inferences, a sample size of 100 is not a strict requirement. However, it is often recommended to have a sample size of at least 100 to ensure that the sample is representative of the population. 4. **Convenience sample**: A convenience sample is a type of non-probability sampling method where the sample is selected based on ease and convenience. This type of sample is not suitable for making statistical inferences because it may not be representative of the population. 5. **Simple random sample**: A simple random sample is a type of probability sampling method where every member of the population has an equal chance of being selected. This type of sample is suitable for making statistical inferences because it is representative of the population. 6. **Systematic sample**: A systematic sample is a type of probability sampling method where every nth member of the population is selected. This type of sample is suitable for making statistical inferences because it is representative of the population. Therefore, the necessary conditions for making a statistical inference are: - Sample size greater than 30 - Approximately normal data set - Simple random sample or systematic sample The other options are not necessary conditions for making a statistical inference.