The alternative is is that it is not equal to zero. This result right here, 1. That's 0.
For each possible value of the theoretical mean, the Z-test statistic has a different probability distribution. So both of these combined are 0. The good news is that, whenever possible, we will take advantage of the test statistics and P-values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course. My idea is to make the background color of my website yellow. In this example, they calculated all of this for us.
So one way to think about it it is a conditional probability. So that's essentially saying it has no effect, because we know that if you don't give the drug the mean response time is 1. But if the null hypothesis was true there's only 1 in chance of getting this. So the standard deviation of our sampling distribution is going to be-- and we'll put a little hat over it to show that we approximated it with-- we approximated the population standard deviation with the sample standard deviation. The hypothesis is no, I think the drug actually does do something. While the above definition is satisfactory for simple hypothesis, we need to be more cautious when dealing with compound hypothesis.
Now there's one last point of clarification that I wanna make very, very, very clear. This is T distribution critical values, so we want to look up 2. In this example, our sample size is six, so six minus one is five, and so we are going to be in this row right over here.
The alternative is is that it is not equal to zero.
The only situation in which you should use a one sided P value is when a large change in an unexpected direction would have absolutely no relevance to your study. Note that the P-value for a two-tailed test is always two times the P-value for either of the one-tailed tests. I say estimate because unlike when we were dealing with proportions, with proportions we can actually calculate the assumed, based on the null hypothesis, sampling distribution standard deviation, but here we have to estimate it. Then of course, Caterina would want to compare that to her significance level that she set ahead of time, and if this is lower than that, then she would reject the null hypothesis and that would suggest the alternative.
And we would also have an alternative hypothesis. It's being derived from these other sample statistics. Then what you want to do is, you want to look up your T value. Now essentially we're just figuring out a Z-score, a Z-score for this result right over there. What we are trying to do is say, "Hey, if we assume the null hypothesis were true, "what is the probability that we got the result "that we did for our sample? So we could say that this is going to be approximately equal to our sample standard deviation divided by the square root of , which is going to be equal to our sample standard deviation is 0.
If you want to estimate sample sizes then you must understand all of the terms mentioned here.