3 An experiment was conducted where rats were given one of f

3. An experiment was conducted where rats were given one of four different diets (labeled A, B, C, and D) at random, and the response variable was liver weight as a percentage of body weight. Here is a summary of the data set:

## liver.weight diet
## Min. :3.350 A:7
## 1st Qu.:3.520 B:8
## Median :3.710 C:6
## Mean :3.718 D:8
## 3rd Qu.:3.870
## Max. :4.310

We wish to test:

H0 µ1 = µ2 = µ3 = µ4

Ha at least one µj is not equal to the others

at the 5% significance level, where µj is the mean liver weight for the population of rats fed on the jth diet, j = 1, 2, 3, 4. Using R, an ANOVA table was computed:

## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = liver.weight ~ diet, data = rats)
##
## $diet
## diff lwr upr p adj
## B-A -0.16571429 -0.45528935 0.1238608 0.4108759
## C-A -0.14738095 -0.45866479 0.1639029 0.5700422
## D-A 0.17678571 -0.11278935 0.4663608 0.3552123
## C-B 0.01833333 -0.28383778 0.3205044 0.9983010
## D-B 0.34250000 0.06274391 0.6222561 0.0122988

Solution

As each p-value is gretaer than the significance level of 0.05, so we will fail to reject the null hypothesis and conclude that all the diets are having similar effects.