Final answer:
The width of a confidence interval for μ is not affected by the sample mean. It is influenced by the confidence level, sample size, and standard deviation, with the confidence level directly affecting the width and sample size and standard deviation influencing the amount of variability and precision.
Step-by-step explanation:
The width of a confidence interval for μ is not affected by D. the sample mean. Factors that do influence the width of a confidence interval include the confidence level, the sample size, and the standard deviation. The confidence level, such as 95%, tells us how confident we can be that the interval includes the true mean. A higher confidence level results in a wider interval. The sample size also affects the width; a larger sample size leads to a narrower interval because it provides more information about the population, reducing variability. The standard deviation reflects the variability within the data set, where a larger standard deviation leads to a wider interval.
An aspect that does not affect the width is the sample mean. The mean itself is the center point of the confidence interval, but it does not influence how spread out the interval is. This is because the width is concerned with precision and certainty regarding the estimate, not the estimate itself.