What is the absolute value of the t statistic for the one-sided test?

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In summary, the Basic F-statistic is a statistical tool used to determine if there is a significant difference between the means of two or more groups in a dataset. It is calculated by dividing the variance between groups by the variance within groups and comparing the ratio to a critical value from the F-distribution. It differs from the t-test in that it can compare more than two groups and takes into account the variability within each group. The significance level for the Basic F-statistic is typically set at 0.05, but can be adjusted. It assumes that the data is normally distributed and that the variances of the groups being compared are equal, and violations of these assumptions may require alternative tests.
  • #1
student007
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Consider the test of the hypotheses:
Null: (sigma1)^2>=(sigma2)^2
Alternative: (sigma1)^2<(sigma2)^2
where α = 0.05 and:
n1 = 8 and s1 = 13.0
n2 = 10 and s2 = 11.5.
What is the test statistic for F?

Your Answer:
1.278
Correct Answer:
1.278

If the alternative hypothesis for two variances has "<", couldn't you switch the s1 and s2 in the f-stat equation to create an upper-tail test? if so, my test statistic would be 0.783
 
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  • #2
F test is a one-sided test. The square root of the F statistic is the absolute value of the t statistic for the one-sided test.
 

1. What is the purpose of the Basic F-statistic?

The Basic F-statistic is used to determine whether there is a significant difference between the means of two or more groups in a dataset. It is commonly used in statistical analysis to test for the overall significance of a regression model or the equality of means in ANOVA.

2. How is the Basic F-statistic calculated?

The Basic F-statistic is calculated by dividing the variance between groups by the variance within groups. This ratio is then compared to a critical value from the F-distribution to determine if the difference between groups is statistically significant.

3. What is the difference between the Basic F-statistic and the t-test?

The Basic F-statistic is used to compare the means of two or more groups, while the t-test is used to compare the means of only two groups. Additionally, the F-statistic takes into account the variability within each group, whereas the t-test does not.

4. What is the significance level for the Basic F-statistic?

The significance level for the Basic F-statistic is typically set at 0.05, meaning that there is a 5% chance of obtaining a result as extreme as the one observed if there is no true difference between the groups. However, the significance level can also be adjusted depending on the specific research question and study design.

5. What are the assumptions of the Basic F-statistic?

The Basic F-statistic assumes that the data is normally distributed and that the variances of the groups being compared are equal. Violations of these assumptions can affect the accuracy of the F-statistic and may require the use of alternative statistical tests.

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