Suppose you know σ and you want an 85 percent confidence level. What value would you use to multiply the standard error of the mean by?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (± .4250) and its Z score to multiply the SEm.
To determine the value to multiply the standard error of the mean (SE) by, in order to achieve a specific confidence level, we need to consult the Z-table.
The Z-table is a statistical tool that provides the critical values of the standard normal distribution (Z-distribution) for different confidence levels. These critical values correspond to specific confidence levels, indicating the area under the curve to the left or right of the critical value.
For an 85 percent confidence level, we need to find the critical value that corresponds to an 85 percent area under the curve. To do this, we calculate the area to the left of the critical value in the Z-distribution.
Since we want the area to the left of the critical value, we look for the value that is closest to 85 percent (0.85) in the Z-table. After finding the closest value, we then determine the corresponding Z-score.
Once we have the Z-score, denoted as Z_w, we can use the formula:
Multiplication factor = Z_w + (Z_w/2)
For an 85 percent confidence level, the Z-table shows that the closest value to 0.85 is 1.036. Therefore, the Z-score is approximately 1.036.
Using the formula mentioned earlier, we multiply the standard error of the mean by the value:
Multiplication factor = 1.036 + (1.036/2) = 1.554
So, to achieve an 85 percent confidence level, you would multiply the standard error of the mean by approximately 1.554.