Question

a simple random sample is drawn from a normally distributed population. the value of which of the following will not be known for certain but can be inferred?
○ μ
○ x̄
○ s
○ n

Explanation:

1. First, recall the definitions:

• \( n \) (sample size) is known as we determine the number of observations in the sample.
• \( \bar{x} \) (sample mean) can be calculated exactly from the sample data.
• \( s \) (sample standard deviation) can be calculated exactly from the sample data.
• \( \mu \) (population mean) is a parameter of the population. When we have a sample from a normally distributed population, we don't know \( \mu \) for certain, but we can infer it (estimate it) using the sample mean \( \bar{x} \) or other inferential statistical methods (like confidence intervals or hypothesis tests).

1. Analyze each option:

• For \( n \): We choose the sample size, so it's known.
• For \( \bar{x} \): Calculated from the sample, so known.
• For \( s \): Calculated from the sample, so known.
• For \( \mu \): It's a population parameter. We can't know it with certainty from a sample, but we can infer (estimate) it using the sample data.

Answer:

\(\mu\) (assuming the options are \( n \) (sample size), \(\bar{x}\) (sample mean), \( s \) (sample standard deviation), and \(\mu\) (population mean))