Question

In one-way ANOVA, if the calculated F value is less than the table F value then:

• A. Reject the hypothesis that the population means are equal
• B. Accept the hypothesis that the population means are equal
• C. Depends on level of significance
• D. Sometimes accept and sometimes reject the null hypothesis

Hint:

In any significance test, if the calculated statistic is less than the critical table value ($\text{Calculated} < \text{Table}$), we fail to reject the null hypothesis.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Hypothesis testing in ANOVA involves comparing an observed test statistic ($F_{\text{cal}}$) against a critical value ($F_{\text{tab}}$) obtained from the F-distribution table at a specified level of significance.

Step 2: Detailed Explanation:
In a one-way ANOVA, the null hypothesis ($H_0$) states that all the treatment population means are equal: \[ H_0: \mu_1 = \mu_2 = \dots = \mu_k \]
The calculated F-value measures the ratio of variance between the treatment groups to the variance within the groups.
If the calculated F-value is less than the critical table F-value ($F_{\text{cal}} < F_{\text{tab}}$), the observed differences between the sample means are not statistically significant.
In this scenario, we do not have sufficient evidence to reject the null hypothesis.
Therefore, we fail to reject (or practically "accept") the null hypothesis that the population means are equal.

Step 3: Final Answer:
We accept the null hypothesis that the population means are equal.