Question

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when is unknown except?

1) Use a t-distribution instead of a z-distribution
2) Use a conservative estimate for the population standard deviation
3) Use a confidence level that is wider than necessary
4) Use a margin of error that is smaller than necessary

Answer 1

When computing the sample size for an interval estimate of a population mean without a known standard deviation, it is recommended to use a t-distribution, a conservative estimate for the population standard deviation, and a wider confidence level. Using a smaller than necessary margin of error is not recommended.

Step-by-step explanation:

To compute the necessary sample size for an interval estimate of a population mean, all of the recommended procedures when the population standard deviation (σ) is unknown except for 'Use a margin of error that is smaller than necessary'. To ensure the accuracy of the interval estimate, the following steps should be taken:

1. Use a t-distribution instead of a z-distribution, which is more appropriate when the population standard deviation is unknown and the sample size is small.
2. Use a conservative estimate for the population standard deviation, which usually means using the sample standard deviation (s) as an estimate for σ if the population standard deviation is unavailable.
3. Use a confidence level that is wider than necessary, which offers a greater assurance that the population mean falls within the confidence interval at the cost of a less precise estimate.
4. Using a margin of error that is smaller than necessary is not recommended, as it might not reflect the true variability in the population, leading to an underestimation of the required sample size.

By applying these steps, the calculated confidence intervals are more likely to include the true population parameter.