Hypothesis Testing

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Prerequisite Materials:

The Binomial Distribution/
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The Normal Distribution
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Hypothesis testing & the Binomial Distribution

1. The null hypothesis, $H_0$, is the hypothesis that you assume to be correct;
2. The alternative hypothesis, $H_1$, tells us about the parameter if your assumption is shown to be wrong;
3. Hypothesis tests with alternative hypotheses in the form $H_1:p<\dots$ & $H_1:p>\dots$ are called one-tailed tests;
4. Hypothesis tests with an alternative hypothesis in the form $H_1:p\ne \dots$ are called two-tailed tests;
5. A critical region is a region of the probability distribution which, if the test statistic falls within it, would cause you to reject the null hypothesis;
6. The critical value is the first value to fall inside of the critical region;
7. The actual significance level of a hypothesis test is the probability of incorrectly rejecting the null hypothesis;
8. For a two-tailed test the critical region is split at either end of the distribution;
9. For a two-tailed test, either double the p-value for your observation, or halve the significance level at the end you are testing.

Hypothesis testing with the normal distribution

For a random sample of size n taken from a random variable $X~N(\mu ,{\sigma }^2)$, the sample mean, $\stackrel{\_}{X}$, is normally distributed with $\stackrel{\_}{X}~N(\mu ,\frac{{\sigma }^2}{n})$.

For the sample mean of a normally distributed random variable, $\stackrel{\_}{X}~N(\mu ,\frac{{\sigma }^2}{n})$, $z=\frac{\stackrel{\_}{X}-\mu }{\frac{\sigma }{\sqrt{n}}}$ is a normally distributed random variable with $z~N(0,1)$.

Questions:

AQA Hypothesis Testing

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