ANOVA An experiment to investigate how different types of feed can affect weight gain in pigs is conducted. This example uses data for pigs which have been randomly assigned to four groups, with each...

ANOVA An experiment to investigate how different types of feed can affect weight gain in pigs is conducted. This example uses data for pigs which have been randomly assigned to four groups, with each group being given a different feed. The response is weight gain as follows:

Using the sample data above, answer the following questions:

a) Specify the null and alternate hypotheses to determine if there is a significant difference between weight gain in pigs given different types of feed.

b) Calculate the test statistic to test your hypotheses and report your result.

c) Specify an appropriate probability of committing a Type I error (α).

d) Report your decision and clearly explain your result

a)

Hypothesis

H₀: µ₁
=
µ₂
=
µ₃
=
µ₄
- There is no significant difference between weight gain in pigs given different types of feed

H_a: µ₁

≠ µ₂
≠ µ₃
≠ µ₄
- There is significant difference between weight gain in pigs given different types of feed

b)

The total sample size is N = 15. Therefore, the total degrees of freedom are:

df_total
= 15-1 = 14

The between groups degrees of freedom are df_between
= 4-1 = 3, and the within groups degrees of freedom are:

Df_within
= df_total
- df_between
= 14 – 3 = 11

First, we need to compute the total sum of values and the mean

The sum of squared value is:

Based on the above calculations, the total sum of squares is:

SS_total
=

= 87403.29 -

= 352.404

The within sum of squares is computes as:

SS_within
=

∑

ss_withingroups
= 18.968+6.648+8.547+42.747 = 76.91

The between sum of squares is:

SS_between

= SS_total
– SS_within
= 352.404 – 76.91 = 275.494