Reading 11- LOS G : Q2 against, class

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2.Consider the regression results from the regression of Y against X for 50 observations:

Y = 0.78 - 1.5 X
The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45.

Which of the following reports the correct value of the t-statistic for the slope and correctly evaluates H₀: b₁ ≥ 0 versus H_a: b₁ < 0 with 95 percent confidence?

A)   t = 3.750; slope is significantly different from zero.

B)   t = -3.750; slope is significantly different from zero.

C)   t = -3.333; slope is significantly negative.

D)   t = 3.333; slope not significantly different from zero.

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The correct answer was C)

The test statistic is t = (-1.5 – 0) / 0.45 = -3.333. The critical t-value for 48 degrees of freedom is +/- 1.667. However, in the Schweser Notes you should use the closest degrees of freedom number of 40 df. which is +/-1.684. Therefore, the slope is different from zero. We reject the null in favor of the alternative.