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s Office conducted a study of how students' involvement into social networks = X measured in hours per week affects their test scores = Y (in a 100-point scale). They assumed all conditions required for this model and used a sample of n = 20 students. As a result, they derived the fitted line equation in the form: Y = 70-2.85 X with the standard error for the estimated slope equal to SE (b) = = 1.5 At the significance level a = 0.05, do they have enough evidence that social networking has ANY impact (positive or negative) on students' test performance? 1. Specify the critical value (or values) required in this case. 2. Formulate Rejection Rule 3. Evaluate the Test Statistic

s Office conducted a study of how students' involvement into social networks = X measured in hours per week affects their test scores = Y (in a 100-point scale). They assumed all conditions required for this model and used a sample of n = 20 students. As a result, they derived the fitted line equation in the form: Y = 70-2.85 X with the standard error for the estimated slope equal to SE (b) = = 1.5 At the significance level a = 0.05, do they have enough evidence that social networking has ANY impact (positive or negative) on students' test performance? 1. Specify the critical value (or values) required in this case. 2. Formulate Rejection Rule 3. Evaluate the Test Statistic

MATLAB: An Introduction with Applications
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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### Analysis of Social Networking Impact on Students' Test Scores The Registrar's Office conducted a study to determine how students' involvement in social networks impacts their test scores. The variable \( X \) represents hours per week spent on social networks, and the variable \( Y \) represents the test scores out of 100. A sample of \( n = 20 \) students was used, and the model derived is: \[ \hat{Y} = 70 - 2.85 \cdot X \] The standard error for the estimated slope is: \[ SE[b] = 1.5 \] **Research Question:** At a significance level of \( \alpha = 0.05 \), is there sufficient evidence that social networking has any impact (positive or negative) on students’ test performance? **Steps to Evaluate the Hypothesis:** 1. **Specify the Critical Value(s):** Determine the critical value(s) required for a two-tailed test at \( \alpha = 0.05 \). 2. **Formulate Rejection Rule:** Define the criteria under which the null hypothesis would be rejected. 3. **Evaluate the Test Statistic:** Calculate the test statistic using the given slope and standard error. 4. **State Decision:** Based on the test statistic and critical value, determine whether to reject or fail to reject the null hypothesis. **Solution:** To be completed by performing statistical tests and calculations based on the steps outlined above.
Transcribed Image Text:### Analysis of Social Networking Impact on Students' Test Scores The Registrar's Office conducted a study to determine how students' involvement in social networks impacts their test scores. The variable \( X \) represents hours per week spent on social networks, and the variable \( Y \) represents the test scores out of 100. A sample of \( n = 20 \) students was used, and the model derived is: \[ \hat{Y} = 70 - 2.85 \cdot X \] The standard error for the estimated slope is: \[ SE[b] = 1.5 \] **Research Question:** At a significance level of \( \alpha = 0.05 \), is there sufficient evidence that social networking has any impact (positive or negative) on students’ test performance? **Steps to Evaluate the Hypothesis:** 1. **Specify the Critical Value(s):** Determine the critical value(s) required for a two-tailed test at \( \alpha = 0.05 \). 2. **Formulate Rejection Rule:** Define the criteria under which the null hypothesis would be rejected. 3. **Evaluate the Test Statistic:** Calculate the test statistic using the given slope and standard error. 4. **State Decision:** Based on the test statistic and critical value, determine whether to reject or fail to reject the null hypothesis. **Solution:** To be completed by performing statistical tests and calculations based on the steps outlined above.
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