Question

Step 1

**Note:**

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Step 2

**Explanation:**

Part (a):

The test hypotheses are:

Null hypothesis: H0: *μ*1 =* μ*2 =* μ*3; vs.

Alternate hypothesis: H1: Treatment means are not all the same.

Part (b):

The *F*-test is used for testing the above hypotheses.

Here, number of treatments, *k* = 3.

Total number of observations, *n* = 6 + 4 + 5 = 15.

Thus, the numerator degrees of freedom for the *F*-distribution is, *k* – 1 = 2; the denominator degrees of freedom, *n* – *k* = 12.

The significance level is, *α* = 0.05.

Thus, the critical value is, *Fα*; *k* – 1, *n* – *k* = *F*0.05; 2, 12.

Using Excel formula, **=F.INV.RT(0.05,2,12)**, the critical value is 3.89.

The decision rule is: Reject H0 if *F* > **3.89**.

Part (c...

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