Question

Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea.

                   

(Data is based on ”Folacin Content of Tea,” J. Amer. Dietetic Assoc., 1983 : 627-632.) Does this data suggest that true average folacin content is the same for all brands?

(a) Carry out a test using α = 0.05 via the P-value method.

(b) Assess the plausibility of any assumptions required for your analysis in part (a).

(c) Perform a multiple comparisons analysis to identify significant differences among brands.

Answer 1

Solution

(a) Carry out a test using α = 0.05 via the P-value method.

Test the null hypothesis : H_0 : There is no significance difference between brand means. with alternative hypothesis

Since H_a : at least one brand mean is different from others. From the given data we have the One-Way ANOVA Table :

We have P-value = 0.027552 < 0.05. So, the null hypothesis is rejected.

Therefore, it can be concluded that there is a significance difference the mean folacin contents in the four brands. This means that at least one brand has average folacin content different from the others.

(b) Assess the plausibility of any assumptions required for your analysis in part (a).

We assume that each of the four brands must follow normal distribution with equal variance.

(c) Perform a multiple comparisons analysis to identify significant differences among brands.

We have

The difference between the pairs and decision are shown in the table below :

       

Therefore, Conclude that there is significant difference between the sample means of the Brand 1 and Brand 4