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10.4 Inference as Decision Tests of significance assess the strength of evidence against the null
- hypothesis. The Pvalue is a probability computed under the assumption
that H0 is true. Using a level of significance ɑ gives us a value at which to make a decision about keeping or rejecting the null hypothesis. If P is less than ɑ than we reject the null hypothesis, if P is greater than ɑ we accept the null hypothesis. Whether this type of decision making is required depends on the situation the statistic is being used in. Acceptance sampling is one situation that requires statisticians to make a decision based on a preset significance level. It involves using a sample to decide if a “batch/population” should be accepted or not. Type I and Type II Errors This is one of the more confusing areas we have to cover. These errors
- ccur because we cannot test an entire population and because not every
sample accurately reflects the population. To look at how this works we are going to look at accepting or rejecting a batch of potato chips. We are given the population mean and standard deviation for salt levels in chips and told that chips whose salt levels do not fall within the 95% confidence interval (ɑ = 0.05) are not
- acceptable. Not every chip can be tested though so a sample from each
batch of chips is tested. H0: the batch of chips meets standards Ha: the batch of chips do not meet standards
- n the basis of a sample from the batch.
We hope our decision is correct but there are two ways we could be wrong ‐ we can accept a bad batch of chips ‐ we can reject a good batch of chips Type I error: Type II error: If we accept H0 (reject Ha) when in fact Ha is true. If we reject H0 (accept Ha) when in fact H0 is true.