Question

which of the following is correct? the width of a confidence interval estimate for a population mean decreases as the confidence level increases. we can decrease the width of a confidence interval estimate for a population mean by decreasing the population standard deviation. a 90% confidence interval estimate for a population mean is wider than an 80% interval estimate to capture the true mean more often. the width of a confidence interval estimate for a population mean increases as the sample size increases.

Answer 1

The width of a confidence interval for a population mean can be decreased by lowering the population standard deviation. A higher confidence level leads to a wider interval, while a larger sample size results in a narrower interval.

Step-by-step explanation:

The correct statement regarding confidence intervals for a population mean is: we can decrease the width of a confidence interval estimate for a population mean by decreasing the population standard deviation. This is because the margin of error in a confidence interval, often denoted as EBM (Error Bound for the Mean), depends inversely on the population standard deviation (σ). Other factors influencing the width of a confidence interval include the confidence level and the sample size.

Increasing the confidence level results in a wider interval because it encompasses a greater proportion of the distribution. Therefore, a 95% confidence interval will be wider than a 90% interval. Conversely, decreasing the confidence level results in a narrower interval since less area under the normal curve is required to capture the true population mean.

Furthermore, increasing the sample size causes the error bound to decrease, making the confidence interval narrower, whereas decreasing the sample size has the opposite effect, resulting in a wider interval.