Arrange the following steps of Hypothesis testing in the proper sequence:

A. Formulate a decision rule to accept the null hypothesis
B. Select the suitable test of significance
C. State the null hypothesis and alternative hypothesis
D. Establish critical or rejection region
E. State the level of significance

Choose the correct answer from the options given below:

Correct option is C

Hypothesis testing follows a structured process to determine whether a hypothesis about a population parameter is valid or not. The correct sequence of steps is:

1. State the Null Hypothesis (H₀) and Alternative Hypothesis (H₁) (Step C)

   • The null hypothesis (H₀) represents a statement of no effect or no difference.

   • The alternative hypothesis (H₁) suggests the presence of an effect or difference.

   • Example:

     • H₀: The average weight of apples is 150g.

     • H₁: The average weight of apples is not 150g.

2. State the Level of Significance (Step E)

   • The significance level (α) represents the probability of rejecting a true null hypothesis.

   • Common values of α are 0.05 (5%) or 0.01 (1%), meaning we are willing to accept a 5% or 1% chance of error.

3. Establish the Critical or Rejection Region (Step D)

   • The critical region is determined based on the chosen significance level.

   • It defines the values of the test statistic that lead to the rejection of H₀.

   • Example: If α = 0.05 in a two-tailed test, the critical values may be ±1.96 for a normal distribution.

4. Select the Suitable Test of Significance (Step B)

   • The appropriate statistical test is chosen based on:

     • The type of data (mean, proportion, variance).

     • Sample size (large or small).

     • Population distribution (normal or skewed).

   • Common tests include the Z-test, t-test, Chi-square test, and ANOVA.

5. Formulate a Decision Rule to Accept or Reject H₀ (Step A)

   • Based on the test statistic and critical value, we decide whether to reject or accept the null hypothesis.

   • If the test statistic falls in the rejection region, H₀ is rejected in favor of H₁.

   • Otherwise, we fail to reject H₀, meaning there is not enough evidence to support H₁.

Thus, the correct sequence is C → E → D → B → A.

Information Booster:

Hypothesis testing is widely used in research, quality control, and decision-making. The null hypothesis (H₀) assumes no effect, while the alternative (H₁) suggests otherwise. The significance level (α) defines the probability of a Type I error (wrongly rejecting H₀). A critical region helps identify significant differences. Choosing the right statistical test is crucial—Z-test for large samples, t-test for small ones. Making the final decision involves comparing the test statistic with the critical value.