In: Statistics and Probability
A study is developed to examine the effects of vitamin and milk supplements on infants weight gain. Four diets are considered: diet A (regular diet plus vitamin supplement) , Diet B(regular diet plus special milk formula ), Diet C ( regular diet plus vitamin supplement and special milk formula ), Diet D is control diet (no special consideration). Twenty infants are selected for the investigation and each is randomized to one of the four competing diet programs, the following table displays weigh gains, measured in kilogram, after 3 months on the assigned diet. (15 points)
Diet A |
Diet B |
Diet C |
Diet D |
2.0 |
1.6 |
2.1 |
1.5 |
1.5 |
1.9 |
2.4 |
2.0 |
2.4 |
2.1 |
1.9 |
1.8 |
1.9 |
1.1 |
1.8 |
1.3 |
2.6 |
1.7 |
2.2 |
1.2 |
Please respond to the following questions
(1) Which tests, one-way or two-way ANOVA is appropriate for the data analysis?
(2) What would be the null hypothesis in this study?
(3) What would be the alternate hypothesis?
(4) Complete the following ANOVA table.
(5) What the conclusion would be if the significant level is set as 0.05?