As an experiment she randomly selected 15 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given a Business Ethics test. At the .01 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?
Students Grades on the Business Ethics Test following the Tutorial
PowerPoint Tutorial AuthorGen Tutorial ABC Tutorial
98 79 65
85 86 73
91 72 78
87 82 66
98 91 71
To determine whether there is a significant difference between how well the different tutorials work for the students, we can perform a statistical test called Analysis of Variance (ANOVA). ANOVA compares the means of three or more groups to determine whether there is a statistically significant difference.
Here's how you can conduct the ANOVA test:
Step 1: State the null and alternative hypotheses:
- Null Hypothesis (H₀): There is no difference between how well the different tutorials work for the students.
- Alternative Hypothesis (H₁): There is a difference between how well the different tutorials work for the students.
Step 2: Determine the test statistic:
In ANOVA, the test statistic is the F-statistic. It compares the variation between the group means to the variation within each group.
Step 3: Set the significance level:
In this case, the significance level is given as α = 0.01.
Step 4: Calculate the F-statistic and the corresponding p-value:
You can use statistical software or a calculator to perform the ANOVA test. The test will provide the F-statistic and p-value. The p-value tells us the probability of observing the data if the null hypothesis is true. If the p-value is smaller than the significance level (α), we reject the null hypothesis.
Given the data:
PowerPoint: 98, 85, 91, 87, 98
AuthorGen: 79, 86, 72, 82, 91
ABC: 65, 73, 78, 66, 71
Step 5: Perform the ANOVA test and interpret the results:
After conducting the ANOVA test, if the p-value is less than 0.01 (α = 0.01), we can conclude that there is a significant difference between how well the different tutorials work for the students. If the p-value is equal to or greater than 0.01, we fail to reject the null hypothesis, meaning there is not enough evidence to conclude that there is a significant difference.
Note: The actual calculations require further mathematical steps and data organization. It is recommended to use statistical software or tools to perform the ANOVA test accurately.