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This lesson extends hypothesis testing to cover the z-test, t-test, tests for proportions, and tests for the difference between two means. These are the core inference procedures in Further Statistics 2.
Every hypothesis test follows the same logical structure:
| Step | Action |
|---|---|
| 1 | State H0 (null hypothesis) and H1 (alternative hypothesis) |
| 2 | Choose significance level α |
| 3 | Calculate the test statistic |
| 4 | Find the critical value or p-value |
| 5 | Make a decision: reject or do not reject H0 |
| 6 | State the conclusion in context |
H0:μ=μ0. Test statistic:
Z=σ/nxˉ−μ0
Compare with zα (one-tailed) or zα/2 (two-tailed).
A manufacturer claims mean weight is 500 g (σ=10). A sample of 36 gives xˉ=497. Test at 5% (two-tailed).
Z=10/36497−500=1.667−3=−1.80
Critical value: z0.025=±1.960. Since ∣Z∣=1.80<1.96, do not reject H0.
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