Hypothesis Testing: Significance Levels Explained
This question relates to hypothesis testing and how the decision changes based on the chosen significance level ($\alpha$).
Understanding Significance Levels
- The significance level ($\alpha$) represents the threshold for rejecting the null hypothesis ($H_0$). It's the probability of making a Type I error (rejecting $H_0$ when it is true).
- Commonly used levels are $\alpha = 0.05$ (5%) and $\alpha = 0.01$ (1%).
- A smaller $\alpha$ (like 0.01) requires stronger evidence to reject $H_0$ compared to a larger $\alpha$ (like 0.05).
Decision Logic
- Given: The null hypothesis could not be rejected at the $\alpha = 0.05$ level. This means the results obtained were not statistically significant enough to discard $H_0$ at the 5% significance level.
- Reasoning: Since the $\alpha = 0.01$ level is more stringent (requires stronger evidence) than the $\alpha = 0.05$ level, if $H_0$ was not rejected at the looser 0.05 level, it certainly will not be rejected at the stricter 0.01 level. The evidence is insufficient for both, and particularly insufficient for the stricter criterion.
- Conclusion: Failing to reject $H_0$ at $\alpha = 0.05$ guarantees that $H_0$ will also not be rejected at $\alpha = 0.01$.
Therefore, the correct conclusion is that the null hypothesis will definitely not be rejected at the .01 level of significance.
Important Questions from Hypothesis testing
Which of the following statements relating to Tests of Hypothesis are correct ? Select the correct code.
Statement I: Type-I error occurs when true null hypothesis gets rejected by the test.
Statement II: Beta value denotes the power of the test.
Statement III : To test the significance of the goodness of fit of a distribution, F-test is applied.
Statement VI: When H0: μM > μF, two-tailed test is applied for testing the hypothesis.
Statement V: The critical value of Z-statistic for two-tailed test at 5% level of significance is 1.96.
Match the items of List-II with the items of List-I and denote the code of correct matching:
List-I
List-II
(a) Testing the goodness of fit of a distribution (i) Z-test (b) Testing the significance of the differences among the average performance of more than two sample groups (ii) Chi-square test (c) Testing the significance of the difference between the average performance of two sample groups (Large-sized) (iii) F-test
Codes:The sequence of steps involved in testing a hypotheses are:
A. Select a suitable test statistic
B. Establish critical or rejection region
C. State the null and alternative hypothesis
D. State the level of significance (α)
E. Formulate a decision rule to evaluate the null hypothesis
Choose the correct answer from the options given below
If α is the level of significance and if (1 − α) is increased, then the width of the confidence interval of mean:
The analysis of variance technique was introduced by:
