Hypothesis Testing and Z-Score Analysis in Statistical Studies

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Hypothesis Testing and Z-Score Analysis in Statistical StudiesStatistics11. The five steps of hypothesis testing are: (1)Specificationof the Null Hypothesis (H0) andtheAlternativeHypothesis (Ha)according to the populations(2)Determine thesignificance level(3)Calculation of the test statistic(4) Calculation of thep-value (5) Conclusion : discard or not the NullHypothesis(1) This step is necessary to define the hypothesis and to recognize the populations that will beconsideredthroughout the study.(2)This step is significant: thesignificant levelgives a position when the Null Hypothesis will beturned down. For example we can choose 5% (or p < 0.05)(3)Calculation of the test statistic. For instance in the case of the Z distribution thez-score iscalculated as followed :𝑧=𝑥−𝜇𝜎(4) Calculation of the p-value, which is the probability of the test statistic. This step is used t find therejection region.(5) The final step compares the score value found previously to the cutoff scoreto say if there is (orthere is not) enough evidence that we can reject (or cannot reject) the Null Hypothesis.14.For these 4 studies we reject the Null Hypothesis in the case: z-score value > z-score cutoff value.A)For the study A : the z-score is𝑧=7−51=2With a 5% significance level the z-score is𝑧0=+1.64then the z-score cutoff value is +1.64.Therefore 2 > 1.64 so we reject the Null HypothesisB)For the study B : the z-score is𝑧=7−51=2With a 5% significance level the z-score is𝑧0=±1.96(two tailed test)then the z-score cutoff value is±1.96Therefore 2 >+1.96so we reject the Null HypothesisC)For the study C : the z-score is𝑧=7−51=2With a 1% significance level the z-score is𝑧0=+2.33then the z-score cutoff value is+2.33Therefore 2 < 2.33 so we fail to reject the Null HypothesisD)For the study D : the z-score is𝑧=7−51=2With a 1% significance level the z-score is𝑧0=±2.58(two tailed test) then the z-score cutoff value is±2.58Therefore-2.58 < 2 < 2.58 so we fail to reject the Null Hypothesis

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