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# 1 Sided T Test | One-tailed And Two-tailed Tests | Inferential Statistics | Probability And Statistics | Khan Academy

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## One-tailed And Two-tailed Tests | Inferential Statistics | Probability And Statistics | Khan Academy

Transcript:

Last time our null hypothesis was, that the drug has no effect. And our alternative hypothesis was, that the drug has one effect. We did not say whether the drug would reduce the reaction time or would raise it. We said that the drug has an effect that the average when we take the drug will not be equal to the average value of the general population. Then the null hypothesis states that the mean with that of the drug will be equal to the mean of the general population, it has no effect. In this situation where we are really just trying to see if has some effect, whether it is extremely positive or not extremely negative effect, both would be considered as effects. We did something called a two-way test. Here is what the two-way test is. Because, frankly, too big reaction time if we had a reaction time which is longer of 3 standard deviations, this would probably also make us to reject the null hypothesis. We dealt with one species with both tails. We could do a similar test of the hypothesis, with the same experiment when there is only one tail. And we could do that when we accept again the null hypothesis is that the drug has no effect. And that the average value of the drug – the average value, and maybe I would say the average value with the drug – it will still be 1.2 seconds, our average response time. If we want to do a one-sided test, but one reason we have already learned that this drug would reduce the reaction time, then our alternative hypothesis … and just get acquainted with the different types of marking, some textbooks or teachers will record the alternative hypothesis as H1, sometimes written as H alternative, both are acceptable. If we want to do a one-sided test, we can say that the drug reduces the reaction time. Or that the average value with the drug is less than 1.2 seconds. If we do a one-sided test this way, we have to decide what we want to look at. We have our sample distribution. In fact, I can use the diagram I made up here. We had a sample distribution of the average value. We know what the average value here, 1.2 seconds, was equal to of the average of the general population. We calculated its standard deviation by the sample standard deviation, and this was justified because we have a sample size greater than 30, so we can still to obtain a normal distribution in the sample distribution. And using that, we saw that the result, the sample mean, which we received, 1.05 seconds is at 3 standard deviations below the mean. If we look – let me portray it again with our new one hypothesis test. And this is the sample distribution. It has an average value here, at 1.2 seconds. And the result we got was 3 standard deviations below the mean. 1,2,3 standard deviations below the mean. This represents those 1.05 seconds. So when we say it that way, we’re not just saying that the drug has an effect – in this case and this was the last consideration, we will look at it from both sides. But here we say that we are only interested in whether the drug reduces reaction time. And just like we did before, we will assume that the drug does not reduce the reaction time. If the drug does not reduce the reaction time, what was the probability or what is the probability that yes decrease so much even more? So here is one tail, just that we are interested in assuming the alternative hypothesis thus, thinking there is a reduction. And if our null hypothesis is true, the probability is yes we get a result more than 1.05 seconds … we are now looking only at this country here. Let’s put it this way. Less than 1.05 seconds, or say, lower. Because last time we were interested in an even more final result, because even a really high score would show that the average value is definitely not 1.2 seconds. In this case, we are interested in the average values, which are lower. And now we are looking for the probability that a result is lower of 1.05 seconds. That means sampling … getting a sample from the sample distribution, which is more than 3 standard deviations below the mean. And in this case we will pay attention to the area from this queue. So this here is going to be a one-sided test of where we are interested in only one direction below the average. If we look at the one-sided test – this area here – last time we saw that these two areas together are 0.3%. But if we pay attention to only one of these areas, if we consider only this one here, it will be half of that, because the normal distribution is symmetrical. So we will have 0.13%. So this here is going to be 0.15%, sorry and if we express it as a decimal fraction, it will be 0.0015. And once again, if we formulate our hypotheses in this way, we would say that if the null hypothesis is true, then there will be a probability of only 0.15% to get a result, lower than the result we obtained. So that would be very unbelievable, which is why we will reject it the null hypothesis and we will accept the alternative. And in this situation P – the value will be 0.0015.

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