Which of the following confidence intervals will be the widest?
a. 90 percent
b. 95 percent
c. 80 percent
d. 98 percent
Which one has the highest percentage?
The width of a confidence interval depends on the level of confidence. The higher the level of confidence, the wider the confidence interval. Therefore, the widest confidence interval would be the one with the highest level of confidence.
In this case, the option with the highest level of confidence is d. 98 percent. So, the widest confidence interval will be a 98 percent confidence interval.
To determine which confidence interval will be the widest, we need to understand how confidence intervals work. A confidence interval is constructed around a point estimate, typically the mean or proportion, and it provides a range within which the true population parameter is likely to fall.
The width of a confidence interval is determined by two factors: the level of confidence and the variability of the data.
In general, as the level of confidence increases, the width of the confidence interval also increases. This is because a higher level of confidence requires a wider range to capture the true population parameter with a higher degree of certainty.
On the other hand, the variability of the data affects the width of the confidence interval in the opposite way. As the variability decreases, the width of the confidence interval decreases as well. This is because less variability means that the data points are closer together, resulting in a narrower range needed to capture the true population parameter.
Now, let's compare the confidence intervals given in the question and determine which one will be the widest:
a. 90 percent: This confidence interval has a lower level of confidence compared to b, d. Therefore, it is likely to be narrower than both.
b. 95 percent: This confidence interval has a higher level of confidence compared to a, c. Therefore, it is likely to be wider than a, c.
c. 80 percent: This confidence interval has a lower level of confidence compared to b, d. Therefore, it is likely to be narrower than both.
d. 98 percent: This confidence interval has a higher level of confidence compared to a, c. Therefore, it is likely to be wider than a, c.
Based on the analysis, the confidence interval with the widest width is option d, 98 percent.