3. An experiment was conducted where rats were given one of four different diets

Question

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

Explanation / Answer

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.

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