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Unformatted text preview: lature has expressed concern about the differences in the
mathematics test scores of high school freshmen across the state. She asks her research
assistant to conduct a study to investigate what factors could account for the differences. The
research assistant looked at a random sample of school districts across the state and used the
factors of percentage of mathematics teachers in each district with a degree in mathematics,
the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090
Analysis of Variance Write the least squares prediction equation.
ŷ = 35.178 + 0.22073x1 + 0.3353x2 + 0.0930x3 AACSB: Analytic
Bloom's: Application
Difficulty: Easy
Learning Objective: 1
Topic: Multiple regression model 11440 Chapter 01  An Introduction to Business Statistics 118. A member of the state legislature has expressed concern about the differences in the
mathematics test scores of high school freshmen across the state. She asks her research
assistant to conduct a study to investigate what factors could account for the differences. The
research assistant looked at a random sample of school districts across the state and used the
factors of percentage of mathematics teachers in each district with a degree in mathematics,
the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090
Analysis of Variance Test the usefulness of variable x1 in the model at α = .05. Calculate the t statistic and state
your conclusions.
t = 3.10. We reject H0 and conclude that x1 is making a significant contribution to predicting
y.
t025,32 = 2.036
t = 0.22073/0.07131 3.10 > 2.036, reject H0 AACSB: Analytic
Bloom's: Application
Difficulty: Hard
Learning Objective: 5
Topic: Significance of an independent variable 11441 Chapter 01  An Introduction to Business Statistics 119. A member of the state legislature has expressed concern about the differences in the
mathematics test scores of high school freshmen across the state. She asks her research
assistant to conduct a study to investigate what factors could account for the differences. The
research assistant looked at a random sample of school districts across the state and used the
factors of percentage of mathematics teachers in each district with a degree in mathematics,
the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090
Analysis of Variance Determine the 90% interval for β2 and interpret its meaning
(0.0135, 0.6571) We are 90% confident that as β2 increases by 1 year, the mathematics test
score will increase by at least 0.0135 points and at most by 0.6571 points.
(b2 ± tsb2) = (0.3353 ± 1.693 (0.1901) = (0.3353 ± 0.3218) = 0.0135 to 0.6571 AACSB: Analytic
Bloom's: Application
Difficulty: Hard
Learning Objective: 5
Topic: Significance of an independent variable 11442 Chapter 01  An Introduction to Business Statistics 120. A member of the state legislature has expressed concern about the differences in the
mathematics test scores of high school freshmen across the state. She asks her research
assistant to conduct a study to investigate what factors could account for the differences. The
research assistant looked at a random sample of school districts across the state and used the
factors of percentage of mathematics teachers in each district with a degree in mathematics,
the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090
Analysis of Variance Based on the multiple regression model given above, estimate the mathematics test score and
calculate the value of the residual, if the percentage of teachers with a mathematics degree is
50.0, the average age is 43 and the average salary is 48,300 (48.3). The actual mathematics
test score for these factors is 68.50.
Estimated test score = 65.12 and residual = 3.38
ŷ = 35.178 + 0.22073 (50) + 0.3353 (43) + 0.0930 (48.3) = 65.12
e = 68.50  65.12 = 3.38 AACSB: Analytic
Bloom's: Application
Difficulty: Hard
Learning Objective: 9
Topic: Residual analysis 11443 Chapter 01  An Introduction to Business Statistics 121. A member of the state legislature has expressed concern about the differences in the
mathematics test scores of high school freshmen across the state. She asks her research
assistant to conduct a study to investigate what factors could account for the differences. The
research assistant looked at a random sample of school districts across the state and used the
factors of percentage of mathematics teachers in each district with a degree in mathematics,
the average age of mathematics teachers and the average salary of mathematics teachers s = 7.62090
Analysis of Variance Additional information related to this point estimate of 65.12 is given below.
Predicted Values for New Observations
50% with math degree, average age of 43 and average salary is 48.3
New Determine the 95% confidence interval for this estimate and interpret its meaning. 11444 Chapter 01  An Introduction to Business Statistics 61.69 to 68.55. We are...
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This document was uploaded on 01/20/2014.
 Winter '14

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