Question

which of the following is correct? 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. the width of a confidence interval estimate for a population mean decreases as the confidence level increases.

Answer 1

The correct answer is that a 90% confidence interval for a population mean is wider than an 80% interval estimate because a higher confidence level requires a larger area under the normal distribution curve.

Step-by-step explanation:

The question is asking which statement correctly describes the characteristics of a confidence interval estimate for a population mean. The correct answer to the question is that a 90% confidence interval estimate for a population mean is wider than an 80% interval estimate to capture the true mean more often. This is due to the fact that with a higher confidence level, we require a larger area under the curve of the normal distribution to ensure that the true population mean is within our interval range.

As for the impact of the population standard deviation and sample size, decreasing the population standard deviation would make the confidence interval narrower, whereas increasing the sample size would make the confidence interval narrower as well, since larger sample sizes reduce the error bound for the mean (EBM).