--- title: "Hypothesis testing steps; computer assemblies" subject: "Probability and Statistics" chapter: 7 key: "semester_5/probability_and_statistics:steps-hypothesis-testing-computers-readjust" source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/steps-hypothesis-testing-computers-readjust site: BCT Engineering --- # Hypothesis testing steps; computer assemblies Probability and Statistics · Chapter 7: Inference concerning proportion - Asked in: 2069 Chaitra, 5 marks - Video: [Hypothesis testing: step-by-step, p-value, t-test for difference of two means - Statistics Help](https://www.youtube.com/watch?v=0zZYBALbZgg) — Dr Nic's Maths and Stats - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/steps-hypothesis-testing-computers-readjust - Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-7 ## Question What are the steps in hypothesis testing? A study shows that 16 of 200 computers produced on one assembly need readjustment before shipping while same happens on 14 out of 300 produced. Test at 1% level of significance that the second assembly is superior than first one? ## Short answer The steps are state H0/H1, choose α, select the test statistic, set critical region, compute the statistic, compare, and conclude. For the assemblies, pooled p̂=0.06, z=1.538 is below the one-tailed 1% critical value 2.326; fail to reject H0, so the second assembly is not shown superior. ## Answer #### Steps in hypothesis testing 1. State the null hypothesis H0 and the alternative hypothesis H1. 2. Choose the level of significance α. 3. Select the appropriate test statistic (z, t, χ² or F) and its sampling distribution. 4. Find the critical value from the table and set the rejection region. 5. Compute the test statistic from the sample. 6. Compare and decide: reject H0 if the value falls in the rejection region, otherwise do not reject. 7. State the conclusion in words. #### Numerical: is the second assembly superior (lower readjustment rate)? ```text Assembly 1: n₁ = 200, x₁ = 16, p̂₁ = 0.0800 Assembly 2: n₂ = 300, x₂ = 14, p̂₂ = 0.0467 Pooled p̂ = 30/500 = 0.06, q̂ = 0.94 ``` 1. H0: p₁ = p₂ H1: p₂ < p₁ (the second assembly needs readjustment less often, so it is superior) 2. α = 0.01 3. Test statistic: ```text SE = √(0.06×0.94×(1/200 + 1/300)) = 0.02168 z = (p̂₁ − p̂₂)/SE = (0.0800 − 0.0467)/0.02168 = 1.538 ``` (z is positive when p̂₁ > p̂₂, matching H1: p₁ > p₂, a right-tailed test.) 4. Critical value: z(0.01, one-tail) = 2.326. Reject H0 if z > 2.326. 5. Decision: z = 1.538 < 2.326 (p-value = 0.062), so **fail to reject H0**. **Conclusion:** at the 1% level, the data do not show that the second assembly is superior to the first. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is the correct order of the first steps in hypothesis testing? A. Compute statistic, state hypotheses, choose alpha B. State H0 and H1, choose alpha, select test statistic C. Choose critical value, state hypotheses, compute statistic D. Conclude, then state hypotheses Answer: B. Hypotheses come first, then the level of significance, then the test statistic, then critical value, calculation and decision. (Key point: Order of steps) 2. To show the second assembly is superior (needs readjustment less often), what is H1? A. p2 > p1 B. p2 < p1 C. p1 = p2 D. p2 not equal p1 Answer: B. Superior means a lower readjustment rate, so H1: p2 < p1, a one-tailed test. (Key point: Alternative hypothesis here) 3. What is the pooled proportion? A. 30/500 = 0.06 B. 16/200 = 0.08 C. 14/300 = 0.0467 D. 0.0333 Answer: A. (16 + 14)/(200 + 300) = 0.06. (Key point: Pooled proportion) 4. z = 1.538 and the one-tail critical value at 1% is 2.326. What is the decision? A. Reject H0; second assembly is superior B. Fail to reject H0; not shown to be superior C. Reject H0 because 1.538 > 1.0 D. Use 2.576 and reject Answer: B. 1.538 < 2.326, so there is insufficient evidence that the second assembly is better. 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