Question

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = $eta_0$ + $eta_1$Age + $epsilon$. The following table summarizes a portion of the regression results. Coefficients Standard Error $t$-stat $p$-value Intercept 56.1772 5.2145 10.7732 0.0000 Age 0.2845 0.0871 3.2671 0.0035 When defining whether age is significant in explaining happiness, the competing hypotheses are $H_0: eta_1 ge 1$; $H_A: eta_1 < 1$ $H_0: eta_1 le 0$; $H_A: eta_1 > 0$ $H_0: eta_1 = 0$; $H_A: eta_1 e 0$ $H_0: eta_1 = 1$; $H_A: eta_1 e 1$

          A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = $eta_0$ + $eta_1$Age + $epsilon$. The following table summarizes a portion of the regression results.
Coefficients Standard Error  $t$-stat  $p$-value
Intercept 56.1772 5.2145 10.7732 0.0000
Age 0.2845 0.0871 3.2671 0.0035
When defining whether age is significant in explaining happiness, the competing hypotheses are
$H_0: eta_1 ge 1$; $H_A: eta_1 < 1$
$H_0: eta_1 le 0$; $H_A: eta_1 > 0$
$H_0: eta_1 = 0$; $H_A: eta_1 
e 0$
$H_0: eta_1 = 1$; $H_A: eta_1 
e 1$

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = eta0 + eta1Age + epsilon. The following table summarizes a portion of the regression results.
Coefficients Standard Error t-stat p-value
Intercept 56.1772 5.2145 10.7732 0.0000
Age 0.2845 0.0871 3.2671 0.0035
When defining whether age is significant in explaining happiness, the competing hypotheses are
H0: eta1 ge 1; HA: eta1 < 1
H0: eta1 le 0; HA: eta1 > 0
H0: eta1 = 0; HA: eta1
e 0
H0: eta1 = 1; HA: eta1
e 1

Added by Cristian P.

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