A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.
a. What are the null and alternative hypotheses (in words, not symbols)?
b. Are the conditions / assumptions for ANOVA met?
c. Calculate the F-statistic.
d. The P-value for this statistic turns out to be

Question

A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.
     a. What are the null and alternative hypotheses (in words, not symbols)?
b. Are the conditions / assumptions for ANOVA met?
c. Calculate the F-statistic.
d. The P-value for this statistic turns out to be < .001. State the conclusion.
e. Suppose the company is concerned about whether different batches of green vegetable material would blanch differently. Suggest how the design for the study could have been improved to take this into account.

Quizplus · Accepted Answer

The Answer is a. H0 : Mean vitamin A retention amounts are equal across the three blanching processes.
HA : Mean vitamin A retention amounts are not all equal across the three blanching processes.
b. We need to assume that the vegetable material samples were randomly assigned to the processes. Boxplots of the original data indicate that the equal variance assumption is reasonable. The normal probability plot of residuals indicates that the normality assumption is reasonable.
c. F = 23.27
d. With such a small P-value, we can reject the null hypothesis and conclude that mean vitamin A retention amounts are not all equal across the different blanching processes.
e. A randomized block design using batch as the blocking variable could improve the study.

A Health Food Company Wants to Determine the Best Process