Final answer:
True, a reduction in the confidence level from 90% to 80% results in a narrower confidence interval for a population mean, since lower confidence levels require less certainty that the interval contains the true mean.
Step-by-step explanation:
True, if the confidence level is reduced from 90% to 80%, the confidence interval for a population mean does become narrower.
The width of the confidence interval is directly related to the confidence level. A higher confidence level means a wider interval because more samples will include the true population mean to ensure that we are within that level of confidence. Conversely, a lower confidence level results in a slimmer interval since we require less certainty that the interval contains the true mean.
As an example, consider a 90% confidence interval that is calculated to be (67.18, 68.82). If we increase the confidence to 95%, the interval becomes (67.02, 68.98), which is wider. This demonstration shows that as the confidence level increases, so does the width of the confidence interval.
To say that we are 90% confident that the true population mean lies within the confidence interval means that if we took repeated samples and constructed intervals in this way, we would expect 90% of them to contain the true population mean.