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Hypothesis testing 1 (Formulating a test (Testing hypotheses (Let X be the…
Hypothesis testing 1
Formulating a test
The null hypothesis, H0, is a statistical statement representing your basic assumption
The alternative hypothesis, H1, is a statement that contradicts the null hypothesis
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One tailed-test: this only tests either below the value stated in H0 or only above the value stated in H0
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Testing hypotheses
Let X be the random variable representing the number of things in the chosen sample who meet the target
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Assuming H0 is true, X is binomially distributed: X~B(n, p)
The critical region is the set of values that leads you to reject the null hypothesis. The acceptance region is the set of values that leads you to accept the null hypothesis
The critical value lies on the border of the critical region. It depecds on the significance level of the test. The critical region includes the critical value and all values that are more extreme than that
Every hypothesis test has a significance level. This is equal to the probability of incorrectly rejecting the null hypothesis
As you lower the significance level, you need more evidence to reject the null hypothesis and you lower the chance of making an incorrect conclusion
Strategy
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2 If the value from the sample lies in the critical region then you reject the null hypothesis. If the value does not lie in the criticaal region the you accept the null hypothesis
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The critical region
If H0 is assumed to be true, for discrete random variables, a value lies within the critical region if the probability of X being equal to or more extreme than that value is equal to or less than the significance level
The p-value is the probability that x is equal to or more extreme than an observed value. If the p-value is greater than the significance level, you accept H0. If the p-value is less than or equal to the significance level, you reject H0
Strategy
1 Define X, state its distribution and write down H0 and H1
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