So the null hypothesis (H 0) is that the process change will not impact the average coating thickness the average coating thickness (μ) will remain at 5. The null hypothesis is set up to assume that nothing changes – that the status quo holds – or in this case, the process change will not impact the average coating thickness. Remember, you want to investigate if the process change will impact the average coating thickness. We will start with the null hypothesis, which is denoted by H 0. You probably have heard of the null hypothesis and alternative hypothesis. Step 1: Formulate the Null Hypothesis and Alternative Hypothesis Now back to the steps in hypothesis testing. We will make use of this knowledge below. These percentages can also be viewed as probabilities, e.g., the probability of getting a result that is less than -1.5 standard deviations below the average is 0.0668. You can determine these percentages from a table of z values (see our publication on the normal distribution) or by using Excel’s NORMSDIST function. To find the percentage of data within z = -1.5 and z = 1.5, you simply use the fact that the area under the curve is 100%, so the percentage of data between the two z values is 100 – 6.68 – 6.68 = 86.64%. If z = 1.5, then the area above z = 1.5 is the percentage of x values that are more than 1.5 standard deviations above the average. For z = -1.5, that area is 6.68% as is shown in Figure 1. The area below z = -1.5 is the percentage of x values that are more than 1.5 standard deviations below the average. The value of z (the z score) is simply how many standard deviations a value, x, is from the average.įor example, suppose x is 1.5 standard deviations below the average. Where x is some value, μ is the average, and σ is the standard deviation of the x values. Any normal distribution can be converted to the standard normal distribution by using the following to calculate z: These two facts can used to help determine the fraction of measurements that fall above some value (such as a specification limit), below some value, or between two values. In addition, the area under the curve is proportional to the fraction of measurements that fall in that region. This special case is called the standard normal distribution and is shown in Figure 1.įor this distribution, the area under the curve from -∞ to +∞ is equal to 1.0. We need to digress a moment here because we will need to make use of a special case of the normal distribution – when the average = 0 and the standard deviation = 1. This will be required when we do some calculations.Ī Brief Pause for the Standard Normal Distribution However, before those steps are covered, a review of the standard normal distribution is needed. The details of the five steps are shown below. The team will go through the basic five steps of hypothesis testing: The team wants to perform a hypothesis test to prove that the average coating thickness will not change. You want to be sure that the coating thickness remains the same before you will approve the process change. The key variable in your process is the thickness of the coating.
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You can download this publication as a pdf here.Ī lean six sigma project team is recommending a change in the coating process you are in charge of to help reduce costs.
A brief pause for the standard normal distribution.This month’s publication takes a look at the five steps involved in conducting a hypothesis test. Note the word “probably.” There is always variation – so there is always a chance for you to make the wrong decision. From there, we have to test the hypothesis and reach a decision if the hypothesis is probably true or probably false. All these things are just statements – just hypotheses. You may claim that the diet plan you created helps people lose more weight than a nationally known diet plan. A drug company can claim that a new drug is better at decreasing blood pressure. So, a hypothesis is just a statement of theory. Or just the opposite hypothesis: getting a flu shot makes no difference in whether someone gets the flu. For example, people who get flu shots are less likely to get the flu. What is a hypothesis? According to the Merriam-Webster’s on-line dictionary, a hypothesis is an idea or theory that is not proven but that leads to further study or discussion.
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