Discussion
For the regression model given below
\(Y = \beta_{0} + \beta_{1}X + U\)
\(Y = 20 + 2X\)
SE : 0.46
To test \(H_{0} : \beta_{1} = 2.1\) against \(H_{1} : \beta_{1} \neq 2.1\) (not equal to 2.1), test statistic \(|t|\) is equal to
Answer: B
The test statistic for the null hypothesis that the slope is 2.1 is the difference between the estimate and the hypothesised value divided by the standard error: \[ |t| = \frac{|2 - 2.1|}{0.46} \] \[ |t| = \frac{0.1}{0.46} \approx 0.217. \] So option B, 0.217, is correct. The value 4.34 is close to 2 divided by 0.46, which is the t value for the null hypothesis that the slope is zero, not 2.1. The estimate of 2 is very near the hypothesised 2.1, so the t value must be small and the null is not rejected, which also rules out 4.609 and 4.34.
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