Question

suppose a researcher knows the population standard deviation is 1.9 and constructs a 90% confidence interval (original interval) for the population mean from a sample of 50 with a sample mean of 10.2. if the researcher wishes to change the confidence level to 96% which of these statements is true about the new confidence interval?

Answer 1

When changing the confidence level from 90% to 96%, the new confidence interval will be wider. This means that the range of values that contains the population mean with a higher level of confidence will be larger.

The reason for this is that as we increase the confidence level, we need to account for a larger range of possible values for the population mean. This wider range increases the margin of error and, consequently, the width of the confidence interval.

Therefore, the true statement about the new confidence interval when changing the confidence level from 90% to 96% is that it will be wider than the original interval.