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Answer :
An introduction to economics course is offered in 3 sections each with different instructor. The average grades given by the instructors were compared to determine if there is a significant difference. We can use analysis of variance (ANOVA) The significance level for the hypothesis test is 0.01.
We compare the means of multiple groups. ANOVA determines if there is a significant difference among the means by analyzing the variation within and between the groups.
Let's denote the average grades for the three sections as X₁, X₂, and X₃. Our null hypothesis (H₀) is that there is no significant difference among the means, while the alternative hypothesis (H₁) is that there is a significant difference. Mathematically, we can state the hypotheses as follows:
H₀: X₁ = X₂ = X₃
H₁: At least one of the means is different
To perform the hypothesis test, we calculate the F-statistic, which is the ratio of between-group variation to within-group variation. If the calculated F-value is greater than the critical F-value, we reject the null hypothesis in favor of the alternative hypothesis.
Using statistical software or a calculator, we can calculate the F-value and compare it to the critical F-value with degrees of freedom based on the number of groups and sample sizes.
If the calculated F-value is greater than the critical F-value, we can conclude that there is a significant difference in the average grades given by the instructors.
To know more about ANOVA refer here:
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