The Summary Statistics for a Certain Set of Points Are $n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614$

question 37

Multiple Choice

The summary statistics for a certain set of points are: $n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614$ , and $b _ { 1 } = 1.29$ Assume the conditions of the linear model hold. A 99% confidence interval for $\beta _ { 1 }$ will be constructed.
Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 0 } : \beta _ { 1 } > 0$ . Use the $\alpha = 0.01$ level of significance.

• A) Reject H₀
• B) Do not reject H₀

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Definitions:

Curve

In economics, it usually refers to a graphical representation of the relationship between two factors, such as supply and demand, price and quantity, etc.

Line

A straight geometrical figure that extends infinitely in both directions without thickness.

Slope

In mathematics, it is the measure of the steepness or incline of a line, defined as the ratio of the vertical change to the horizontal change between two points on the line.

Positive Economics

A branch of economics that focuses on objective analysis and the description of how the economy functions, as opposed to normative economics that involves value judgments.