given the following information, determine the 68.3 percent, 95.5 percent, and 99.7 percent confidence intervals. Mean = 4.33, standard error of the mean =3
% = mean ± ? SEm
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability ([1-%]/2) and its Z score. Enter Z score for ?.
Solve for intervals.
To determine the confidence intervals, we need to consider the sample mean and the standard error of the mean. The confidence intervals represent a range of values within which we can be fairly confident that the true population parameter lies.
1. 68.3 percent confidence interval:
The 68.3 percent confidence interval, also known as the one standard deviation interval, includes a range of values that covers approximately 68.3 percent of the population. To calculate it, we'll use the formula:
CI = mean ± (standard error * 1)
Substituting the given values:
CI = 4.33 ± (3 * 1)
CI = 4.33 ± 3
CI = (1.33, 7.33)
Therefore, the 68.3 percent confidence interval is (1.33, 7.33).
2. 95.5 percent confidence interval:
The 95.5 percent confidence interval, also called the two standard deviation interval, includes a range of values that covers approximately 95.5 percent of the population. Using the formula:
CI = mean ± (standard error * 2)
Substituting the given values:
CI = 4.33 ± (3 * 2)
CI = 4.33 ± 6
CI = (-1.67, 10.33)
So, the 95.5 percent confidence interval is (-1.67, 10.33).
3. 99.7 percent confidence interval:
The 99.7 percent confidence interval, also known as the three standard deviation interval, includes a range of values that covers approximately 99.7 percent of the population. Using the formula:
CI = mean ± (standard error * 3)
Substituting the given values:
CI = 4.33 ± (3 * 3)
CI = 4.33 ± 9
CI = (-4.67, 13.33)
Hence, the 99.7 percent confidence interval is (-4.67, 13.33).