F Distribution and One-Way ANOVA

What is the primary purpose of a one-way ANOVA (Analysis of Variance) test?

According to Section 12.1, which two conditions must be true to perform an F test of two variances?

If the null hypothesis for a test of two variances is that the population variances are equal, what does the F-ratio become?

A study compares the grade variances of two instructors. Instructor 1's grades have a variance of 52.3 from a sample of 10 exams. Instructor 2's grades have a variance of 89.9 from a sample of 10 exams. What is the F statistic for testing if the first instructor's variance is smaller?

What is the alternative hypothesis (Ha) for a one-way ANOVA test?

In the context of ANOVA, what does MSbetween (Mean Square Between) represent?

If a one-way ANOVA test has 4 groups and a total of 40 samples, what are the degrees of freedom for the numerator (df(num)) and the denominator (df(denom))?

What does it mean if the F-ratio in a one-way ANOVA test is approximately equal to one?

Which of the following statements about the F distribution is correct?

In an experiment comparing five mulching conditions for tomato yields, the calculated F statistic is 4.4810. With a significance level of 5 percent, and a critical F value of 3.26, what is the correct decision?

What does a balanced design in the context of one-way ANOVA signify?

If you perform an F test of two variances and the F statistic is much larger than one, what does this suggest?

In a one-way ANOVA test, the calculated p-value is 0.0248 and the pre-set significance level (alpha) is 0.05. What is the correct decision and conclusion?

For a test of two variances, if the test is left-tailed, how is the lower tail critical value found using an F-table that only provides upper tail values?

In a one-way ANOVA, what is the relationship between the total sum of squares (SStotal), the sum of squares between groups (SSbetween), and the sum of squares within groups (SSwithin)?

Why is the one-way ANOVA hypothesis test always right-tailed?

A study is conducted on three diet plans. The ANOVA table shows SS(between) = 2.2458 with df = 2, and SS(within) = 20.8542 with df = 7. What is the Mean Square for Error (MSwithin)?

The F test for equality of two variances is noted to be very sensitive to what deviation from its assumptions?

In a one-way ANOVA, what is MSwithin also known as?

If a test of two variances has 15 samples in the first group and 21 samples in the second group, what are the degrees of freedom for the numerator (df1) and denominator (df2) respectively, using the shorthand method?

A one-way ANOVA is conducted on 3 groups with 10 observations each (30 total observations). The SStotal is 23.1 and the SSbetween is 2.2458. What is the SSwithin?

What is the population mean for an F distribution with df(num) = 4 and df(denom) = 16?

The F distribution is a ratio of what two other distributions?

What type of variable is the 'factor' in a one-way ANOVA test?

A test of two variances is conducted with n1 = 25 and n2 = 16. What are the degrees of freedom for the test?

In the ANOVA table for the tomato experiment (Table 12.7), the test statistic F is 4.4810. How is this value calculated?

If two populations are being compared and are found to have different population means but equal variances, which assumption of one-way ANOVA is met?

In Example 12.5, comparing bean plants, the calculated F statistic was 0.134. With a 3 percent significance level, the conclusion was to not reject the null hypothesis. Why?

An F test for two variances gives a test statistic of F = 0.716. The test is a two-tailed test with df1=24 and df2=24. If the upper critical value F_alpha/2 is 2.27, what can you conclude?

What is the relationship between the F statistic and the p-value in a one-way ANOVA test?

A one-way ANOVA is conducted on 5 groups. The total number of observations is 25. What are the degrees of freedom for the denominator (within groups)?

An ANOVA test on four sports teams' GPAs results in an F statistic of 2.23 and a p-value of 0.1241. Using a 5 percent significance level, what is the conclusion?

What is the key difference between the 'variance between samples' and 'variance within samples' in an ANOVA context?

If a study is comparing the mean sales of three different stores, what would the null hypothesis (H0) for a one-way ANOVA be?

Two instructors grade the same 10 exams. The first instructor's grades have a variance of 52.3, and the second's have a variance of 89.9. What are the degrees of freedom for this test of two variances?

Why might a supermarket be interested in using a test of two variances?

In a one-way ANOVA table, how is the Mean Square (MS) for a source of variation calculated?

If the null hypothesis is true in a one-way ANOVA test, what should be the approximate relationship between MSbetween and MSwithin?

A study on the heights of singers in a choral society is conducted. For the Tenor1 group, n=9 and variance is 16. For the Bass2 group, n=9 and variance is 25. What is the F-statistic to test if the variances are different, using the shorthand method?

What is the key takeaway from the visual representation of ANOVA in Figure 12.3, which shows box plots?

For the ANOVA on three diet plans in Example 12.2, with SS(between) = 2.2458 and SS(total) = 23.1, what percentage of the total variation is explained by the difference between the diet plans?

If you conduct a one-way ANOVA and the p-value is 0.001, what does this imply?

When comparing two sample variances, if the test statistic F is calculated as s1^2 / s2^2, the degrees of freedom are df1 = n1-1 and df2 = n2-1. What does the notation F ~ F(n1 – 1, n2 – 1) signify?

A researcher is comparing the mean weights of three groups of men. What would be an appropriate random variable for a one-way ANOVA test?

If a one-way ANOVA on four groups yields df(denom) = 16, and each group had an equal number of samples, how many total observations were there?

An ANOVA test is performed with MS(between) = 172.08 and MS(within) = 110.87. What is the calculated F statistic?

When the null hypothesis of a one-way ANOVA is false, which of the following is generally expected?

If you are comparing the mean salaries of graduates from five different universities, which statistical test is most appropriate?

Why might a finance professional use a test of two variances?

An F-test for two variances is conducted with n1=10 and n2=10. The calculated test statistic is 1.719. What is the critical value at a 10 percent significance level for this one-tailed test?