Please help!!!
Smith Widget Company makes widgets for the medical industry. One particular customer requires widgets that meet FDA standards. One FDA standard requires Z-testing of at least 100 widgets at a time at the .08 level of significance. The specific standard requires that widgets be no smaller than a certain tolerance and no larger than a certain tolerance. The critical value(s) for such a test would be:
If you are doing a z-test, you look at a z-table for your cutoff or critical value(s). How do you translate .08 to a cutoff value from the table? It depends on whether the test is one-tailed or two-tailed. For a two-tailed test (cutoff points at both tails), you split the .08 into .04 and .04 for both tails. (For a one-tailed test, you don't split the value.) Some z-tables will make it easier for you by showing values in the tails. Then you would look for your cutoffs according to the level given, remembering to split for two-tailed tests. It may also help to have an index card with some commonly used cutoff values, so you don't have to look at the table each time.
To find the critical value(s) for a Z-test with a significance level of 0.08, we need to refer to the standard normal distribution table or use a statistical calculator.
The critical value(s) for a one-tailed Z-test at the 0.08 significance level can be found by:
1. Determining the area in the tail (alpha) by subtracting the significance level from 1. In this case, alpha = 1 - 0.08 = 0.92.
2. Finding the Z-score that corresponds to the alpha value obtained in step 1. This can be done by looking up the value in the standard normal distribution table or using a calculator.
Assuming a one-tailed test (since we are only concerned with widgets smaller than the tolerance), we need to find the Z-score that corresponds to an area of 0.92.
Using a standard normal distribution table, we find that the Z-score corresponding to an area of 0.92 is approximately 1.4051.
Therefore, the critical value(s) for this Z-test at a significance level of 0.08 would be +1.4051 (since we are considering only widgets smaller than the tolerance).
Note: If it were a two-tailed test, we would need to find the Z-scores at alpha/2 on both sides of the distribution.