Question

At the 0.025 significance level, do the data provide sufficient evidence to conclude that a difference exists between the population means of the three different brands? The sample data are given below.

Brand A	Brand B	Brand C
32	27	22
34	24	25
37	33	32
33	30	22
36		21
39

Answer options:

		A) 0.01 < p-value < 0.025 Reject Null
		B) p-value < 0.005 Reject Null
		C)0.005 < p-value < 0.01 Reject Null
		D) p-value > 0.05 Do Not Reject Null

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.025.

Analyze sample data.

F statistics is given by:-

F = 12.123

F_critical = 3.89

The P-value = 0.00132

Interpret results. Since the P-value (0.00132) is less than the significance level (0.025), we have to reject the null hypothesis.

B) p-value < 0.005

Reject Null

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the three brands.