when making a statistical inference about the mean of a normally distributed population based on a sample…
when making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population, which of the following statements is correct, all else being equal?\nthe 68% confidence interval is wider than the 90% confidence interval.\nthe 90% confidence interval is narrower than the 95% confidence interval.\nthe 90% confidence interval is wider than the 99% confidence interval.\nthe 99% confidence interval is narrower than the 68% confidence interval.
Answer
Brief Explanations:
As the confidence level increases, we want to be more certain that the population mean lies within the interval. To achieve higher certainty, the interval needs to be wider to capture more possible values of the population mean. So, a 90% confidence interval is narrower than a 95% confidence interval because a 95% confidence interval requires a higher level of certainty and thus is wider.
Answer:
The 90% confidence interval is narrower than the 95% confidence interval.