Question

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Explanation:

Identify the core requirements for inference

Using the Statistical Inference Assumptions knowledge point
To make valid statistical inferences about a population from a sample, certain fundamental conditions must be met. The two primary requirements are:

1. Randomization: The data must be collected using a random sampling method (such as a simple random sample) to avoid bias and ensure the sample is representative of the population.
2. Normality/Sample Size: The sampling distribution of the estimator must be approximately normal. This is satisfied if the population is normally distributed or if the sample size is sufficiently large (typically \(n \ge 30\)) by the Central Limit Theorem.

Evaluate the given options

• "sample size greater than 30, or an approximately normal data set": This is a necessary condition to satisfy the normality assumption for the sampling distribution of the mean.
• "sample size greater than 100": This is not a strictly necessary condition; \(n \ge 30\) is generally sufficient for the Central Limit Theorem.
• "convenience sample": This is a non-random sampling method that introduces bias, making statistical inference invalid.
• "simple random sample": This is a necessary condition to ensure that the sample is representative and free from selection bias, which is foundational for statistical inference.
• "systematic sample": While a probability sampling method, it is not a universally required criterion like a simple random sample or general randomization.

Thus, the necessary conditions listed among the choices are a simple random sample and a sample size greater than 30, or an approximately normal data set. Since this is a multi-select question (indicated by square checkboxes), both of these correct criteria should be selected.

Answer:

• [x] sample size greater than 30, or an approximately normal data set (Correct answer)
• [ ] sample size greater than 100
• [ ] convenience sample
• [x] simple random sample (Correct answer)
• [ ] systematic sample