Final answer:
To calculate the margin of error for a confidence interval when the population standard deviation is unknown, we use the sample mean and sample standard deviation, and rely on the Student's t-distribution. The margin of error involves these statistics and the appropriate t-score for the desired confidence level.
Step-by-step explanation:
In constructing a confidence interval for a single unknown population mean (μ), when you do not have prior knowledge about the value of the population standard deviation (σ), the correct distribution to use is the Student's t-distribution rather than the normal distribution. This choice is made because the Student's t-distribution provides a more accurate confidence interval for cases where the population standard deviation is unknown and the sample size is small.
Within the context provided by the question, the variables you use in the calculation of the margin of error (EBM) are the sample mean (x) and the sample standard deviation (s). The formula for the margin of error in a t-distribution confidence interval involves the sample mean, the sample standard deviation, and the t-score that corresponds to the desired confidence level.
The margin of error (EBM) calculation will therefore rely on:
- The sample mean (x), as the point estimate of the unknown population mean (μ).
- The sample standard deviation (s), which is used as an estimate for the population standard deviation (σ).
- The t-score from the t-distribution that corresponds to the desired confidence level.
Given these points, the answer to the question of which of these is used in the calculation of the margin of error is 'f. Standard deviation of the sample' and 'e. Normal distribution' if population standard deviation is known or Student's t-distribution if it is not.