Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression TestScore = 483.9720+ (-5.4126) × CS, R ² = 0.10, SER = 10.7 (18.9720) (2.0553) Construct a 95% confidence interval for B₁, the regression slope coefficient. The 95% confidence interval for B₁, the regression slope coefficient, is (☐, ☐). (Round your responses to two decimal places.) The t-statistic for the two-sided test of the null hypothesis Ho: B₁ = 0 is Note: Assume a normal distribution. The p-value for the two-sided test of the null hypothesis Ho: B₁ = 0 is Do you reject the null hypothesis at the 1% level? ○ A. Yes, because the t-statistic is greater than 2.58. B. Yes, because the p-value is less than 0.01. C. Yes, because the t-statistic is less than 2.58. D. No, because the p-value is greater than 0.01. (Round your response to four decimal places.) (Round your response to four decimal places.) The p-value for the two-sided test of the null hypothesis Ho: B₁ = -5.2 is (Round your response to four decimal places.) Without doing any additional calculations, determine whether - 5.2 is contained in the 95% confidence interval for B₁. A. Yes, - 5.2 is contained in the 95% confidence interval for B₁. B. No, -5.2 is not contained in the 95% confidence interval for ẞ₁. The 99% confidence interval for ẞo is ). (Round your responses to one decimal place.) 2
Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression TestScore = 483.9720+ (-5.4126) × CS, R ² = 0.10, SER = 10.7 (18.9720) (2.0553) Construct a 95% confidence interval for B₁, the regression slope coefficient. The 95% confidence interval for B₁, the regression slope coefficient, is (☐, ☐). (Round your responses to two decimal places.) The t-statistic for the two-sided test of the null hypothesis Ho: B₁ = 0 is Note: Assume a normal distribution. The p-value for the two-sided test of the null hypothesis Ho: B₁ = 0 is Do you reject the null hypothesis at the 1% level? ○ A. Yes, because the t-statistic is greater than 2.58. B. Yes, because the p-value is less than 0.01. C. Yes, because the t-statistic is less than 2.58. D. No, because the p-value is greater than 0.01. (Round your response to four decimal places.) (Round your response to four decimal places.) The p-value for the two-sided test of the null hypothesis Ho: B₁ = -5.2 is (Round your response to four decimal places.) Without doing any additional calculations, determine whether - 5.2 is contained in the 95% confidence interval for B₁. A. Yes, - 5.2 is contained in the 95% confidence interval for B₁. B. No, -5.2 is not contained in the 95% confidence interval for ẞ₁. The 99% confidence interval for ẞo is ). (Round your responses to one decimal place.) 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression
TestScore = 483.9720+ (-5.4126) × CS, R ² = 0.10, SER = 10.7
(18.9720) (2.0553)
Construct a 95% confidence interval for B₁, the regression slope coefficient.
The 95% confidence interval for B₁, the regression slope coefficient, is (☐, ☐). (Round your responses to two decimal places.)
The t-statistic for the two-sided test of the null hypothesis Ho: B₁ = 0 is
Note: Assume a normal distribution.
The p-value for the two-sided test of the null hypothesis Ho: B₁ = 0 is
Do you reject the null hypothesis at the 1% level?
○ A. Yes, because the t-statistic is greater than 2.58.
B. Yes, because the p-value is less than 0.01.
C. Yes, because the t-statistic is less than 2.58.
D. No, because the p-value is greater than 0.01.
(Round your response to four decimal places.)
(Round your response to four decimal places.)
The p-value for the two-sided test of the null hypothesis Ho: B₁ = -5.2 is
(Round your response to four decimal places.)
Without doing any additional calculations, determine whether - 5.2 is contained in the 95% confidence interval for B₁.
A. Yes, - 5.2 is contained in the 95% confidence interval for B₁.
B. No, -5.2 is not contained in the 95% confidence interval for ẞ₁.
The 99% confidence interval for ẞo is
). (Round your responses to one decimal place.)
2
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