Can someone please help me with this?
Consider that you are examining the relationship between the height of children and their parents. You decide to collect data from 110 college students, and estimate the following relationship :
(hat) Studenth = 19.6 + 0.73 × Midparh
with R2 = 0.45, the Standard Error of the Regression (SER) = 2.0, standard error for the intercept is (7.2) and for the slope is (0.10), where StudentHeight is the height of students in inches, and AveragePaentHeight is the average of the parental heights. Both variables were adjusted so that the average female height was equal to the average male height.
How do you set for the statistical significance of the slope coefficient?
Hints:
$H_0: \beta_1=0$
$H_1:\beta_1 >0$
The test-value is t-distributed, if $H_0$ is true.
$t_{emp}=\frac{b_1}{s_{B1}}=\frac{0.7}{0.1}=7$
The critical value is $t_c=t_{(\alpha,n-2)}$. It is a one-sided t-test.
If $t_{emp}>t_c$, the Null-Hypothesis should be rejected at a significance level of $\alpha$. Otherwise the Null-Hypothesis has to be not rejected.