Certain Metal™ Testing a new manufacturing process
What is the question of interest? • Previous to the change in process 20% of the ingots manufactured were cracked. If the new process has the same proportion then the new process is not better. If the new process is better then the proportion will drop… • Significantly! • So we will determine if the proportion has dropped and if so is the drop significant.
Ok, so what is the null hypothesis? • The null hypothesis is the proportion of cracked ingots from the previous process. • We will reject this hypothesis if we see the new process producing a proportion which is significantly less. • The alternate hypothesis is the new hypothesis which represents a meaningful improvement in the process. We will never accept this but we may reject the null in favor of it.
Now we will perform a One Proportion Z-test. • You will have to sample the ingots produced using the new process. • Remember the sample size must be large enough to meet the conditions of the Central Limit Theorem (CLT) • The collection of the sample must be random to avoid bias. (no taking just the pretty ones)
Experimental Design PhaseThis is the part of the study where you collect data. It is crucial to give this part the most thought. It is a real challenge to design a data collection process that avoids bias. For this study we will program the factory computer to set 400 ingots aside based on a randomizing process.
Testing the conditions Since we know
In our sample of 400 we find 68 cracked ingots. This gives us our sample proportion.
Ok so the proportion is lower, but is it significantly lower? Changing the process of casting for large scale production is expensive so we want moderately strong evidence that the new process is going to result in a lower proportion of cracked ingots.We chose a significance level of 1%.
Next we compute the standard deviation, this is based on the assumption that the null hypothesis is true.
Test StatisticThis is the standardized observation or z-score of the sample proportion and helps us determine how likely we could get a sample like this if the null hypothesis is true.
Calculate the “P” valueP stands for probability. We get this right from the z table or your calculator.
Decision TimeThis is where we decide if our observation is significantly different than the null hypothesis.We will reject the null hypothesis if the probability of the drawing the sample we drew is less than the significance level we determined. Since the significance level is commonly denoted by alpha which looks a little like a fish some clever person came up with…
If P eats the fish, reject the Ho!Ok, weird but memorable.If the P-value is less than our significance value we will reject to null hypothesis.
ConclusionSince we cannot reject the null hypothesis we must conclude that our sample proportion is not significantly low enough to ensure that the new process will result in a lower proportion of cracked ingots. The management can not claim victory! This doesn’t mean we accept the null hypothesis, we simply cannot reject it in favor of our alternate.
Another viewWe can include in our report a confidence interval based on our sample. I am going to make it a 99% confidence interval to mach our significance value.