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Sample Size - Coggle Diagram
Sample Size
Alpha value
What are the costs associated with an unnecessary change if the team makes a mistake in rejecting the null hypothesis?
o Inamanufacturingenvironment,whatarethecostswithrejectingmaterialsthat actually fit specifications?
o Inanon-manufacturingenvironment,whatarethecostsassociatedwithacceptingthe hypothesis that change did occur?
Are there dangers or costs associated with concluding that a statistical change occurred? What are they?
type 2
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A Type II error occurs when you accept the null hypothesis when it is, in fact, not true. If you accept the hypothesis that the sample mean is statistically the same as the hypothesized mean when, in fact, the sample mean is statistically greater than the hypothesized mean, then you have a Type II error.
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selecting beta value
What is the potential costs of a Type II error if the team makes a mistake in not rejecting the null hypothesis?
o Whatisthepotentialdamageorcostifdefectivematerialsarepassedtothecustomer? If a defective spoon is passed along, the ultimate cost might be minimal compared to a defective piece of medical equipment or car engine.
o Aretherecostsassociatedwithlosttimeorresourcesincorrectingaproblemthat comes from a Type II error?
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Six Sigma teams take samples because they want to determine information about a population. With some exceptions, it is very difficult, very expensive, or impossible to run statistical calculations on the entire population of data.
The uncertainty associated with sampling is defined by something called the Confidence Interval, which is also called the margin of error in some applications.
Type I Error
A Type I error occurs when you reject the null hypothesis during a hypothesis test when, in fact, the null hypothesis is true. You might reject the null hypothesis that the mean of the sample is statistically the same as the hypothesized mean, deciding instead that the sample mean is statistically greater than the hypothesized mean.
Before you can move onto calculating sample size, some practical considerations must be made with regard to alpha, beta, and delta. In our review of Type I and Type II errors, we covered the difference between producer and consumer risks, but that breakdown doesn’t work in all organizations or with all hypothesis tests.