Test the linear contrast in part (h) using the Schefle lest for general contrasts, and write YOur conclusion_ Be sure tO state the null and the alternative hypothes...

State the null hypothesis, $H_{o},$ and the alternative hypothesis, $H_{a},$ that would be used to test the following statements: a. The linear correlation coefficient is positive. b. There is no linear correlation. c. There is evidence of negative correlation. d. There is a positive linear relationship.

So, um, we're supposed to write a null hypothesis and an alternate hypothesis, so I'm going to write it on here. No hypothesis. Alternate hypothesis, though the first statement is that, um, the slope of the line of best fit is positive. So the slope is greater than zeer. Or the null hypothesis would be that the slope equals zero. Let's do the next one up. You just down. Give me space to write all three of them. Okay. The slope of the line is not significant. Well, definitely. Slope of the line is not significant. Slope of the line is significant. The last one says the negative slope for the regression line is significant. All right, so all we gotta do is copy it up here and right is not so to be more clear. And you can see this An example. 13.9. Um, when it says, um, the slope of the line of best fit is significant. Is it significant enough? Then we would write Slope is greater than zero. If it's significant. Slope equals zero. If it's insignificant and the same thing down here, except you would write negative slope so negative one times the slope. Negative one. I am so slow now. Also, we have to decide whether we know whether these slopes are going to be positive or negative. And we need to decide whether we're going to use a one tailed test or to tail, so it would be just as reasonable to write. The slope is less than zero. If you expected to be less than zero, the opposite of the slope is, um, less than zero if you'd expect it to be less than zero.

This time. I alternative hypothesis is mu greater than two. So what will be my null hypothesis? My null hypothesis will be immune less than equal to. And if I want to draw it, this is to this is one. This is zero and so on. So my two is included and everything toe the left off it on the number line. This will be my answer.

In this case, my alternative hypothesis is mule less than three. So what will be my null hypothesis? My age not will be mu greater than equal to three. So if I want this on a number line, this will look something like this. The graph will be three for five six and so on. Three will be included and greater than three. This will be my answer.