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Mashutka [201]
3 years ago
5

A study was conducted to compare the effect of three diet types on the milk yield of cows (in lbs). The sample size, sample mean

, and sample variance for each method are given below.
Diet A: n1 = 9, X1 = 39.1, s21 = 24.6
Diet B: n2 = 8, X2 = 29.9, s22 = 16.4
Diet C: n3 = 10, X3 = 45.9, s21 = 10.3
(a) Construct an ANOVA table including all relevant sums of squares, mean squares, and degrees of freedom.
(b) Perform an overall F test to determine whether the population means of milk yield are the same or not among the three diet types.

Mathematics
1 answer:
Vlad [161]3 years ago
6 0

Answer:

(a) Anova table is attached below.

(b) The population means of milk yield are different among the three diet types

Step-by-step explanation:

In this case we need to perform a One-way ANOVA to determine whether the effect of three diet types on the milk yield of cows are significantly different or not.

The hypothesis can be defined as follows:

<em>H</em>₀: The effect of three diet types on the milk yield of cows are same.

<em>Hₐ</em>: The effect of three diet types on the milk yield of cows are significantly different.

(a)

The formulas are as follows:

\text{Grand Mean}=\bar x=\frac{1}{3}\sum \bar x_{i}\\\\SSB=\sum n_{i}(\bar x_{i}-\bar x)^{2}\\\\SSW=\sum (n_{i}-1)S^{2}_{i}\\\\N=\sum n_{i}\\\\DF_{B}=k-1\\\\DF_{W}=N-k\\\\DF_{T}=N-1\\

The F critical value is computed using the Excel formula:

F critical value=F.INV.RT(0.05,2,24)

The ANOVA table is attached below.

(b)

The rejection region is defined as follows:

F > F (2, 24) = 3.403

The computed F statistic value is:

F = 34.069

F = 34.269 > F (2, 24) = 3.403

The null hypothesis will be rejected.

Thus, concluding that the population means of milk yield are different among the three diet types

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