A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of 18 18 students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. State the null and alternative hypotheses for a one-way ANOVA test.

Welcome back to The Practice. Let's just dive right in. In this problem, a school administrator is interested in seeing if three educational methods, traditional, flipped, and online, are equally effective. So the administrator takes 18 random test scores evenly distributed amongst the three methods at the end of the semester and is interested in using that data to perform a one way ANOVA test, which will allow him to compare the means across those three different methods. For this problem, we wanna state the null and alternative hypotheses for this ANOVA test. Remember that the null hypothesis for our ANOVA test is going to be that all means are the same. So I can represent this with symbols, and I'm gonna use mu sub t to be the average test score for traditional method. I'm gonna represent average test score for flipped method to be mu sub f and the average test score for the online method to be mu sub o. So to represent this with symbols, I can say mu sub t is equal to mu sub f is equal to mu sub o. All of the means are the same. Now our alternative hypothesis will be that the null hypothesis isn't true, so all of the means are not the same. This means that at least one mean is different. And often what we'll do when we have a specific scenario that we wanna build an alternative hypothesis for is we'll just introduce some of the specifics from the scenario into our alternative hypothesis. So I'm just gonna rewrite this as at least one method has a different average test score. Awesome. Now very quickly, I just wanna reiterate the fact that the ANOVA test is not able to tell us if it is just one mean is different or if all three of the means are different. The ANOVA test will also not be able to tell us which mean, if it is only one, is the one that is significantly different. All it can tell us if we accept the alternative hypothesis is that at least one of those means is different. Awesome work. Why don't you head over to the next practice if you're feeling ready?

A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of 18 18 students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. State the null and alternative hypotheses for a one-way ANOVA test.

H 0 H_0 : All students perform equally well on the final exam, regardless of the instructional method. H 1 H_1 : At least one group of students performs differently than the others.

H 0 H_0 : The three instructional methods lead to different mean exam scores. H 1 H_1 : All three instructional methods lead to the same mean exam scores.

H 0 H_0 : There is a significant difference among the teaching methods. H 1 H_1 : There is no significant difference among the teaching methods.

A school administrator wants to examine whether students' academi...

14. ANOVA

Introduction to ANOVA

Statistics

14. ANOVA

Introduction to ANOVA

Struggling with Statistics?

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Multiple Choice

A school administrator wants to examine whether students' academic performance differs based on the type of instructional method used in their classes. A random sample of $18$ students is selected and divided evenly among the three teaching methods. After a semester, all students take the same standardized final exam. State the null and alternative hypotheses for a one-way ANOVA test.

$H sub 0$ : All means are the same

$H_{A}$ : At least one mean is different, at least one method has a different average test score.

$H sub 0$ : All students perform equally well on the final exam, regardless of the instructional method.

$H sub 1$ : At least one group of students performs differently than the others.

$H sub 0$ : The three instructional methods lead to different mean exam scores.

$H sub 1$ : All three instructional methods lead to the same mean exam scores.

$H sub 0$ : There is a significant difference among the teaching methods.

$H sub 1$ : There is no significant difference among the teaching methods.

Verified step by step guidance

Step 1: Understand the problem. The school administrator wants to determine if students' academic performance differs based on the type of instructional method using a one-way ANOVA test. The data provided includes test scores for three instructional methods: Traditional, Flipped, and Online.

Step 2: Define the null and alternative hypotheses for the one-way ANOVA test. The null hypothesis (H₀) states that all group means are equal, meaning the instructional method does not affect academic performance. The alternative hypothesis (H₁) states that at least one group mean is different, indicating that the instructional method affects academic performance.

Step 3: Organize the data. The test scores for each instructional method are provided in the table. Calculate the mean and variance for each group (Traditional, Flipped, Online) to prepare for the ANOVA test.

Step 4: Perform the one-way ANOVA test. Compute the between-group variance (how much the group means differ from the overall mean) and the within-group variance (how much individual scores differ within each group). Use these variances to calculate the F-statistic.

Step 5: Compare the F-statistic to the critical value from the F-distribution table at the chosen significance level (e.g., α = 0.05). If the F-statistic exceeds the critical value, reject the null hypothesis (H₀) and conclude that at least one instructional method leads to different academic performance.

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