MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Select the correct null and alternative hypotheses.**
1. \( H_0: \mu < 78\% \)
\( H_a: \mu \geq 78\% \)
2. **\( H_0: p \geq 78\% \)**
**\( H_a: p < 78\% \)**
3. \( H_0: p < 78\% \)
\( H_a: p \geq 78\% \)
4. \( H_0: \mu \geq 78\% \)
\( H_a: \mu < 78\% \)
)
**Scenario**
At the conclusion of the semester, the standard method of instruction yielded 100 grades with a mean final grade of 74.161% and a standard deviation of roughly 10.78%. A mathematics professor in the department stated that he thinks, on average, students score a 78% in the first-year algebra course; however, the mean from the sample data suggests that the true average could be lower. Answer the following questions to determine if the true population mean is lower than 78% at the 5% significance level. Since experimental methods were used in “Method 1” and “Method 2”, these grades will be ignored. *Only grades from the “Standard Method” will be considered.*](https://content.bartleby.com/qna-images/question/edd99afd-48e9-4e8a-b434-1d3cd4c035a5/091c49d5-ab0f-4b23-84d9-e6007267a96b/210xau_processed.png)
Transcribed Image Text:**Background**
In a previous lab, the results of a study conducted at a large university were presented. It compared the effectiveness of two alternative teaching methods in first-year algebra courses: “Method 1” and “Method 2”. To ensure that the selected methodology benefited all first-year students at the university, the committee conducted a randomized trial.
Three sections of the course were opened: one where a professor taught the material in a standard way, one where a professor taught using Method 1, and one where a professor taught using Method 2. Students were then randomly assigned to one of the three algebra courses but were not told that the methods of instruction varied. (Each method was assigned 100 students.) After the completion of these courses, the final grades of the students were compiled into a database. This database was used to decide which instructional method will be implemented in future classes.
**Data**
The “comma separated variable” (csv) file containing (fictitious) students’ final grades is included below. It is entitled “TestScores(2).csv” and can be downloaded. This dataset contains 300 values divided into three columns: standard method, new method 1, and new method 2. These labels correspond to the teaching strategies implemented in the scenario described above. Use descriptive statistics to characterize these data and draw conclusions. (Data: [TestScores(2).csv](#))
**Scenario**
At the conclusion of the semester, the standard method of instruction yielded 100 grades with a mean final grade of 74.161% and a standard deviation of roughly 10.78%. A mathematics professor in the department stated that he thinks, on average, students score a 78% in the first-year algebra course; however, the mean from the sample data suggests that the true average could be lower. Answer the following questions to determine if the true population mean is lower than 78% at the 5% significance level. Since experimental methods were used in “Method 1” and “Method 2”, these grades will be ignored. *Only grades from the “Standard Method” will be considered.*
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