Hypothesis testing without the jargon
Hypothesis testing is a fixed recipe wrapped in intimidating language. Once the five steps are automatic, the exam questions become mechanical.
What this covers
- Null and alternative hypotheses
- Test statistics: z, t, chi-square
- p-values and significance levels
- Type I and Type II errors
- Confidence intervals
Worked example
Problem
A machine should fill 500 ml. A sample of 36 bottles averages 495 ml, Ο = 12. Test at Ξ± = 0.05.
- 1State hypothesesHβ: ΞΌ = 500, Hβ: ΞΌ β 500 (two-tailed).
- 2Compute the test statisticz = (495 β 500) / (12/β36) = β5/2 = β2.5.
- 3CompareCritical values at Ξ± = 0.05 two-tailed are Β±1.96; p β 0.0124 < 0.05.
- 4Conclude in contextReject Hβ β evidence the machine is underfilling.
Answer: Reject Hβ at the 5% level (z = β2.5, p β 0.012)
Mistakes that cost marks
- Saying you 'accept' the null hypothesis instead of failing to reject it.
- Halving or doubling the p-value for the wrong tail.
- Concluding statistically without stating the context.
Questions students ask
What does a p-value actually mean?
The probability of data at least this extreme if the null hypothesis were true β not the probability the null is true.
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