Answered: racing bikes. Brand Weight Price ($) A…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section: Chapter Questions

Problem 13CR

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$## Data Analysis of Road-Racing Bikes Consider the following data on $ x = \text{weight (pounds)} $ and $ y = \text{price (\$)} $ for 10 road-racing bikes. | Brand | Weight (lbs) | Price ($) | |-------|--------------|-----------| | A | 17.8 | 2,100 | | B | 16.1 | 6,350 | | C | 14.9 | 8,370 | | D | 15.9 | 6,200 | | E | 17.2 | 4,000 | | F | 13.1 | 8,600 | | G | 16.2 | 6,000 | | H | 17.1 | 2,680 | | I | 17.6 | 3,400 | | J | 14.1 | 8,000 | These data provided the estimated regression equation: \[ \hat{y} = 28,506 - 1,433x \] - **Sum of Squared Errors (SSE):** 7,009,621.71 - **Total Sum of Squares (SST):** 51,682,800 Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance. ### Hypotheses State the null and alternative hypotheses: 1. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 \neq 0 $ 2. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 > 0 $ 3. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 < 0 $ Find the value of the test statistic. (Round your answer to two decimal places.) \[ \boxed{} \]$

Transcribed Image Text:## Data Analysis of Road-Racing Bikes Consider the following data on $ x = \text{weight (pounds)} $ and $ y = \text{price (\$)} $ for 10 road-racing bikes. | Brand | Weight (lbs) | Price ($) | |-------|--------------|-----------| | A | 17.8 | 2,100 | | B | 16.1 | 6,350 | | C | 14.9 | 8,370 | | D | 15.9 | 6,200 | | E | 17.2 | 4,000 | | F | 13.1 | 8,600 | | G | 16.2 | 6,000 | | H | 17.1 | 2,680 | | I | 17.6 | 3,400 | | J | 14.1 | 8,000 | These data provided the estimated regression equation: \[ \hat{y} = 28,506 - 1,433x \] - **Sum of Squared Errors (SSE):** 7,009,621.71 - **Total Sum of Squares (SST):** 51,682,800 Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance. ### Hypotheses State the null and alternative hypotheses: 1. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 \neq 0 $ 2. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 > 0 $ 3. $ H_0: \beta_1 = 0 $ $ H_a: \beta_1 < 0 $ Find the value of the test statistic. (Round your answer to two decimal places.) \[ \boxed{} \]