**Scenario: Statistics Class Performance Comparison**A statistics teacher has conducted a large introductory class over many years, with an enrollment of 500 students. The mean score across all these students for the first midterm was $ \mu = 78 $ with a standard deviation $ \sigma = 10 $. One particular year, the teacher opted to teach a much smaller class consisting of only 25 students. The objective was to determine if teaching a smaller class leads to better student performance. This small class can be considered as a Simple Random Sample (SRS) from the larger group of students historically taking the class. For the smaller class, the average midterm score achieved was $ \bar{x} = 83 $.**Formulating the Hypothesis**The hypothesis options are as follows:1. $ H_0: \mu = 78 $ vs. $ H_a: \mu > 78 $2. $ H_0: \mu = 78 $ vs. $ H_a: \mu = 88 $3. $ H_0: \mu = 88 $ vs. $ H_a: \mu < 88 $4. $ H_0: \mu = 88 $ vs. $ H_a: \mu = 78 $**Selection Guide**The teacher aims to investigate whether the smaller class size results in a statistically significant increase in average student scores. Therefore, the hypothesis should reflect testing whether the smaller class's average score is greater than the long-standing average of the larger class.

Name: **Scenario: Statistics Class Performance Comparison**A statistics tea
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Description: **Scenario: Statistics Class Performance Comparison**A statistics teacher has conducted a large introductory class over many years, with an enrollment of 500 students. The mean score across all these students for the first midterm was $ \mu = 78 $

Solution: From the given information, µ=78, σ=10 and n=25. Here, the students wanted to know if…

Math

Statistics

A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was u = 78 with standard deviation o = 10. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was x = 83. The hypothesis should be: Но : и %3D 78 vs. Ha : и> 78. О Но : и 3D 78 vs. Ha : и 3 88. Но : и 3D 88 vs. Ha : и < 88. O Ho : µ = 88 vs. Ha : µ = 78.

A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was u = 78 with standard deviation o = 10. One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was x = 83. The hypothesis should be: Но : и %3D 78 vs. Ha : и> 78. О Но : и 3D 78 vs. Ha : и 3 88. Но : и 3D 88 vs. Ha : и < 88. O Ho : µ = 88 vs. Ha : µ = 78.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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