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The estimated score will be between

The estimated score will be between

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 4CA
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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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