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### Course: Statistics and probability>Unit 12

Lesson 5: More significance testing videos

# One-tailed and two-tailed tests

Sal continues his discussion of the effect of a drug to one-tailed and two-tailed hypothesis tests. Created by Sal Khan.

## Want to join the conversation?

• Shouldn't the sum of your rejection regions in your two tailed test (0.3%) should be the same as the rejection region in your one tailed test (0.3%) and not the 0.15% as stated in the video? So the area of a rejection region in a one tailed test is alpha, but in a two tailed test is alpha/2? Also note that the two hypothesis have to be mutually exhaustive. In other words the null hypothesis should be greater than or equal to the default mean of 1.2 seconds and not just simply equal to. Thanks!
• Yes, I noticed this problem too. The sum of the two tails should be .3% but when using a single tailed test, the region of rejection (alpha) should equal .3% as well.
• To me, it seems like we would get the same answer if had the alternative hypothesis that the drug is raising response time. But this seems very counter-intuitive since the sample mean from the rats on drugs is lower than the population mean when the rats are not on drugs. Wouldn't this indicate that it more probable that the drug lowers response time rather than raising response time? Is P(drug lowers response time) = P(drug raises response time)? And why/why not?
• I totally agree, if we use the same logic we would end up with the same probability that drug raises response time.
Any idea how to resolve this problem?
• So, would it be fair to say that doing a one-tailed test leaves you more room to conclude that the alternative hypothesis is true? That is, when you did the one tailed test the p value wound up being even more extreme than with the two tailed test, so we could have actually had a slower response time (closer to the mean) and still have had the same p-value as in the two tailed test.
• Off the bat it could be said that a one-tailed test leaves more room to conclude that the alternative hypothesis is true. To decide if a one-tailed test can be used, one has to have some extra information about the experiment to know the direction from the mean (H1: drug lowers the response time). If the direction of the effect is unknown, a two tailed test has to be used, and the H1 must be stated in a way where the direction of the effect is left uncertain (H1: the drug has an effect on the response time).

A one tailed test does not leave more room to conclude that the alternative hypothesis is true. The benefit (increased certainty) of a one tailed test doesn't come free, as the analyst must know "something more", which is the direction of the effect, compared to a two tailed test.
• what identification of z-test and t-test?
(1 vote)
• It's important to state that the t-test is used when the sample number is less than 30 since there is a z-test that's used when you only have the sample standard deviation but the sample number is equal or greater than 30.
• Hi, everyone!

Quick question: What if we decided that our alternative hypothesis claimed that the drug increases the time response. Wouldn't we have still had a p-value of 0.0015 and, thus, rejected the null hypothesis and accepted the alternative? Isn't this inconsistent? I appreciate all the help that I can get! Thanks!
• I don't feel confused about this. If we were that wrong about our experiment, I think we ought to simply change to a two tail framing of the problem - that is: What's the probability that the drug has some effect (which allows for either increase or decrease in response time).
(1 vote)
• How would you know when to use the left tail test or the right tail test.
For example if a company claims a drug makes you lose atleast 20 pounds in a month. A sample of 20 were used sith mean 15 and standard deviation 4! Test the company claim at 1 percent?
How would i know its a left tail test and how would u write the null hypothesis and solve it?
• the word (atleast ) means that the value will be greater then or equal to 20 , And in alternative hypothesis we only use "<" , ">" and not equal sign . so in this question the given information tell us that this is :
Null Hypothesis : μ ≥ 120
alternative hypothesis : μ < 120
• When comparing one-tailed and two-tailed p-values, would the area under the curve for the one-tailed not be 0.3 and then the two-tailed be 0.15? Why would your one sided only be 0.15 if the actual total area under the curve is equivalent in both one-tailed and two-tailed?

Just confused because in class, we were taught that if your p-value for significance in less than 0.05, for a two tailed test, your areas in the two sides are 0.025 which collectively make up 0.05. Thanks!
• The 2 tails are 1 for z < -3, and 1 for z > 3. Which is larger - both added together or either one by itself? What is larger - .0030 or .0015?
(1 vote)
• what can be said about the 2 sided p-value for testing the null hypothesis of no change in cholesterol levels, if on average after three months the cholesterol levels among 100 patients decreased by 15.0 and standard deviation of the changes in cholesterol was 40.
thanks.
• sample std=40
std sampling distribution=4
sample mean=15/4=3.75std less than population mean
ie outside the critical region or the 99.87% confidence interval and one can reject the null hypothesis . P value= .0013 one sided test.
• Why is the standard deviation of the mean different than the mean of the sample? Isn't sampling distribution just a distribution of the sample? why does that change the mean?