Need help with these questions: I have already answered 27 out of the 30 accept these last three:

8. Given the significance level 0.01, the F-value for the degrees of freedom, d.f. = (7,3) is.

A) 8.45
B) 27.67
C) 5.89
D) 14.62

9. One-way ANOVA is performed on three independent samples with: n1 = 6, n2 = 7 , and n3 = 8. The critical value obtained from the F-table for this test at the 2.5% level of significance equals:
A) 3.55
B) 39.45
C) 4.56
D) 29.45

10. A randomized block design ANOVA has five treatments and four blocks. The computed test statistic (value of F) is 4.35. With a 0.05 significance level, the appropriate table value and conclusion will be:

A) 14.37: accept the null hypothesis
B) 3.11: accept the null hypothesis
C) 3.26: accept the null hypothesis
D) 3.26: reject the null hypothesis

a

b
c
d

All of these questions require you to read the F-distribution table for the values stated. I'll give you a few hints and see if you can take it from there.

For #8:
It's either A or B. Read the table using the degrees of freedom and significance level as guidelines.

For #9:
Degrees of freedom is 2, 18 (for a one-way Anova). Check the table.

For #10:
If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, then do not reject the null.

I hope this will help get you started.

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To answer these questions, we need to have access to the F-table or understand how to calculate the F-value using the degrees of freedom.

For Question 8:

The F-value can be calculated using the formula F = (SSB / (k - 1)) / (SSE / (n - k)), where SSB is the between-group sum of squares, SSE is the within-group sum of squares, k is the number of groups, and n is the total sample size.

In this case, the degrees of freedom for the numerator (SSB) are 7 and for the denominator (SSE) are 3.

To calculate the F-value, we need to look up the critical F-value in the F-table with degrees of freedom (7,3) at a significance level of 0.01.

The critical F-value is the value at which the area in the upper tail of the F-distribution equals the significance level.

Using the table or a statistical software, we find that the critical F-value is approximately 8.45.

Therefore, the correct answer is A) 8.45.

For Question 9:

One-way ANOVA tests for the equality of means in three or more groups. To determine the critical value for this test, we need to find the appropriate F-value from the F-table with degrees of freedom (k-1, n-k) at a significance level of 0.025 (2.5% divided by 2 for a two-tailed test).

In this case, we have 3 groups, so k = 3, and the degrees of freedom are (2, 18) using the formula (n1-1, n - k), where n1, n2, and n3 are the sample sizes.

Using the table or a statistical software, we find that the critical F-value is approximately 3.55.

Therefore, the correct answer is A) 3.55.

For Question 10:

In a randomized block design ANOVA, the F-value can be calculated using the formula F = (SSB / (k - 1)) / (SSE / (b - 1)), where SSB is the between-group sum of squares, SSE is the within-group sum of squares, k is the number of treatments, and b is the number of blocks.

In this case, there are 5 treatments and 4 blocks. The computed test statistic (value of F) is 4.35.

To determine the appropriate F-value from the F-table at a significance level of 0.05, we need to find the critical F-value with degrees of freedom (k-1, (k-1)(b-1)).

Using the table or a statistical software, we find that the critical F-value is approximately 3.26.

Since the computed test statistic (4.35) is higher than the critical F-value (3.26), we reject the null hypothesis.

Therefore, the correct answer is D) 3.26: reject the null hypothesis.