Final answer:
A 95% confidence interval is wider than a 90% confidence interval, and for the given data on mortality rate of the 1918 H1N1 pandemic, the narrower 90% CI, centered around the same point estimate as the 95% CI, would be (0.63, 0.65), which is option a.
Step-by-step explanation:
When constructing confidence intervals (CIs) for a population parameter, such as a mortality rate, a higher confidence level results in a wider interval. This is because a higher confidence level means we want to be more certain that our interval contains the true population parameter. Given that a 95% confidence interval for the mortality rate of the 1918 H1N1 flu pandemic is (0.62, 0.66), if we then construct a 90% confidence interval using the same data set, the interval will be narrower because it contains less of the total probability and thus has a smaller margin of error. We exclude 5% at each tail for a 90% CI instead of 2.5% in the case of a 95% CI.
The correct confidence interval in this scenario would therefore be one that is narrower than the given 95% CI but still centered around the same point estimate. Therefore, the correct 90% CI option would be (0.63, 0.65), which is option a. Options b, c, and d are either too wide or have shifted center points, which isn't consistent with simply decreasing the confidence level.
In summary, larger confidence levels correspond to wider intervals, and the narrower 90% confidence interval for this data set could be correctly represented by option a (0.63, 0.65).