What is the decision at a 0.05 level of significance for each of the following t

Question

What is the decision at a 0.05 level of significance for each of the following tests? Hint: Find the critical value for each test; then make a decision. (Round your critical values to two decimal places.) E Part (a) F(3, 27)#3.01 Fone cri Retain the null hypothesis. O Reject the null hypothesis. E Part (b) F(5, 23) 2.42 Font O Retain the null hypothesis. Reject the null hypothesis. Part (c) F(4, 39)- 268 Fore cri Retain the null hypothesis. Reject the null hypothesis. a Part (d) F(2, 13)#373 O Retain the null hypothesis Reject the nuil hypothesis.

Explanation / Answer

(a)

In this case,degrees of freedom: df1 = 3, df2 = 27

Statistic, F = 3.01

Significance level, a = 0.05

So the critical F-value is:

Fcrit = 2.96

Since F > Fcrit, reject the null hypothesis.

(b)

In this case,degrees of freedom: df1 = 5, df2 = 23

Statistic, F = 2.42

Significance level, a = 0.05

So the critical F-value is:

Fcrit = 2.64

Since F < Fcrit, retain the null hypothesis.

(c)

In this case,degrees of freedom: df1 = 4, df2 = 39

Statistic, F = 2.68

Significance level, a = 0.05

So the critical F-value is:

Fcrit = 2.61

Since F > Fcrit, reject the null hypothesis.

(d)

In this case,degrees of freedom: df1 = 2, df2 = 13

Statistic, F = 3.73

Significance level, a = 0.05

So the critical F-value is:

Fcrit = 3.81

Since F < Fcrit, retain the null hypothesis.

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