The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____.

Question

BlackTom AI · Accepted Answer

The question asks which factor is not involved in determining the expression used to compute an interval estimate of μ.
Option 1: 'whether there is sampling error' — This is the correct choice. The presence or absence of sampling error is not a parameter that changes the form of the interval formula itself; rather, sampling error is what interval estimates aim to quantify. The expression (z-interval or t-interval) is chosen based on other factors, and the notion of sampling error is an inherent aspect of interval estimation, not a condition that alters the algebraic form.
Option 2: 'whether the population has an approximately normal distribution' — This matters, especially for small sample sizes. If the population is approximately normal or the sample size is large enough, you can use the z or t procedures with corresponding assumptions. So this factor influences which formula you apply.
Option 3: 'whether the population standard deviation is known' — This is crucial. If σ is known, you typically use a z-based interval; if σ is unknown, you use a t-based interval with sample standard deviation s, which changes the expression.
Option 4: 'the sample size' — The sample size determines whether the t distribution or the z distribution is appropriate and also affects the width of the interval; thus, it directly influences the expression used.
In summary, the expression chosen for the interval depends on normality considerations, whether σ is known, and the sample size, while the mere existence of sampling error is not a decision point that changes the form of the interval formula itself.

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____.Single choice

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