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The estimated score will be between

The estimated score will be between

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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### Predicting Test Scores Based on Study Hours This exercise involves analyzing the relationship between study hours and test scores for a group of students in Mr. Phelp's 7th-grade math class. The goal is to use this data to predict a student's score who studies for 2 hours. #### Data Table The table below shows the number of hours studied and the corresponding test scores: | Hours Studied (x) | Test Score (y) | |-------------------|----------------| | 5 | 65 | | 6 | 71 | | 7 | 78 | | 8 | 82 | | 9 | 86 | | 10 | 94 | #### Regression Analysis A regression analysis was conducted to establish the relationship between hours studied and test scores. The results are summarized as follows: - **Regression Equation:** \(\hat{y} = 5.543x + 37.762\) - **Standard Error of Estimate:** \(S_e = 1.13\) - **Sums for calculations:** - \(\sum(x) = 45\) - \(\sum(x^2) = 355\) #### Margin of Error and Prediction Interval Using this regression equation, the task is to calculate the 80% prediction interval of a student's score who studied for just 2 hours. This involves selecting the appropriate range of scores with a given margin of error. #### Possible Prediction Ranges The potential estimated score intervals, with their corresponding margins of error, are provided below: - **Option A:** 48.848 to 51.796, with a margin of error of 2.838 - **Option B:** 46.010 to 51.686, with a margin of error of 2.838 - **Option C:** 40.357 to 46.253, with a margin of error of 2.948 - **Option D:** 45.900 to 48.848, with a margin of error of 2.768 - **Option E:** 45.900 to 51.796, with a margin of error of 2.948 The correct range should be selected based on the regression equation and the given standard error to accurately reflect the predicted score for 2 hours of study.
Transcribed Image Text:### Predicting Test Scores Based on Study Hours This exercise involves analyzing the relationship between study hours and test scores for a group of students in Mr. Phelp's 7th-grade math class. The goal is to use this data to predict a student's score who studies for 2 hours. #### Data Table The table below shows the number of hours studied and the corresponding test scores: | Hours Studied (x) | Test Score (y) | |-------------------|----------------| | 5 | 65 | | 6 | 71 | | 7 | 78 | | 8 | 82 | | 9 | 86 | | 10 | 94 | #### Regression Analysis A regression analysis was conducted to establish the relationship between hours studied and test scores. The results are summarized as follows: - **Regression Equation:** \(\hat{y} = 5.543x + 37.762\) - **Standard Error of Estimate:** \(S_e = 1.13\) - **Sums for calculations:** - \(\sum(x) = 45\) - \(\sum(x^2) = 355\) #### Margin of Error and Prediction Interval Using this regression equation, the task is to calculate the 80% prediction interval of a student's score who studied for just 2 hours. This involves selecting the appropriate range of scores with a given margin of error. #### Possible Prediction Ranges The potential estimated score intervals, with their corresponding margins of error, are provided below: - **Option A:** 48.848 to 51.796, with a margin of error of 2.838 - **Option B:** 46.010 to 51.686, with a margin of error of 2.838 - **Option C:** 40.357 to 46.253, with a margin of error of 2.948 - **Option D:** 45.900 to 48.848, with a margin of error of 2.768 - **Option E:** 45.900 to 51.796, with a margin of error of 2.948 The correct range should be selected based on the regression equation and the given standard error to accurately reflect the predicted score for 2 hours of study.
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