Skip to main content

Hypothesis testing steps; computer assemblies

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.

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?

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)?

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:
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.)

  1. Critical value: z(0.01, one-tail) = 2.326. Reject H0 if z > 2.326.
  2. 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.

✓ Answer checked by Claude Sonnet 5.5

Related questions

All Probability and Statistics chapter 7 questions →