The rejection region is the space(s) on the normal graph that contain values whose probabilities are less than alpha. The region(s) are placed where the z score lies on the graph and continue away from the hypothesized mean. It could be one side or both. This defines the rejection region. The P value is the probability that a sample will fall in the area between the rejection regions or to the right of a left tail or to the left of a right tail.
To reject the null hypothesis, the P value you find must be below the given alpha. Failing to reject the Ho means the P value (probability of an occurrence) is greater than the alpha value given.
Statisticians are often asked to do these types of hypothesis tests for a very good reason. This helps determine if companies are just blowing smoke or if their claims are based on real findings and trials. There may be a hospital claiming to have a success rate of 95% for a certain procedure. A hypothesis test based on a random sample of previous procedures at that hospital could determine whether or not that claim is true.
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A rejection region, defined by the textbook, is the range of values within a sampling distribution for which the null hypothesis is not probable. If the value of the hypothesis falls within this range the hypothesis is rejected. If it does not fall within the range, the hypothesis fails to be rejected. It is related to the z-score because it separates the rejection region from the non rejection region. It is related to the p-value because the p-value is compared to the significance level (alpha) to determine whether or not the hypothesis is rejected.
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