Author Question: Suppose a test procedure about the population mean is performed, when the population is normal with ... (Read 43 times)

genevieve1028 · **on:** Jun 24, 2018

Suppose a test procedure about the population mean is performed, when the population is normal with an unknown variance, and a sample of size 20 is drawn from the population.

If the alternative hypothesis is H1 : > 0, then the null hypothesis is rejected at a level = 0.05 if t > 1.729. Indicate whether the statement is true or false

Question 2

Discuss the conceptual basis of using a t-test for inferences about the population slope parameter.

How does this t-test relate to the t-test for the correlation coefficient and the F test for the significance of the model? Do all these relationships make sense?

gabrielle_lawrence · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

TRUE

Answer to Question 2

What we are testing is whether the sample slope statistic is significantly far enough away from 0 to say that the true population slope is significantly different from 0. The sample slope b1 has a normal distribution and that leads to a t-test for the slope where the standard error of b1 is estimated by s . If the t statistic is big enough or small enough then the true slope differs significantly from 0. This t-test statistic is exactly equivalent to the t-test statistic for the correlation. That is because, if the true slope is 0, then based on the model, Y does not depend on X and so they are not correlated. On the other hand, if the correlation is 0, there is no linear relationship between X and Y and hence according to the model, the true slope must be 0. Moreover, the F test for the significance of the model is also equivalent to these t-tests because (tn-2)2 = F1,n-2. Of course, if the model is not significant, that means that Y does not depend on X and thus the slope and the correlation coefficient are all 0.