One-tailed T Test | One Tailed And Two Tailed Tests, Critical Values, & Significance Level – Inferential Statistics

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One Tailed And Two Tailed Tests, Critical Values, & Significance Level - Inferential Statistics


How do you know when you’re supposed to use a one-tailed test or a two-tailed tests? Let’s say when you’re solving problems associated with hypothesis testing. How do you know well in this video? We’re going to talk about that, So let’s say that a company manufactures potato chips and that the average mass of each potato chip bag is a hundred grams, so that is going to be the null hypothesis, where the mean Mu is a hundred grams. Now let’s say that an employee believes this answer to be different. He believes that the mean is not 100 grams so this is going to be the alternative hypothesis. Now, whenever you have the situation whenever the alternative hypothesis doesn’t equal some value, you’re going to have a two-tailed tests, so let’s draw a picture of that, so we have a normal distribution and we’re going to shade the area on the left and on the right. So this is a two-tailed test. The shaded area represents the rejection region, the area that is not shaded is the fail to reject region Now the Z values that separate these two regions, the rejection region and the fail to reject region Those Z values are known as critical values. Now let’s say that the employee conducts the tests at a 95% confidence level. C is going to be 0.9 5 C is equal to 1 minus Alpha. So that’s the confidence level Alpha is going to be the significance. Level C Plus Alpha is 1 so 1 minus 0.9 5 That’s point 0 5 That’s Alpha. This is known as the significance level so because Alpha is split into two regions. The right side is going to be Alpha over 2 and the left side is Alpha over 2 each with an area of point 0 to 5 The area in the middle is 0.95 now, in order to determine whether you should be checked or not reject the null hypothesis. You need to calculate the Z value and compare it to the critical value. So this other Z value. Let’s call it a ZC. This is gonna be the calculated Z value, which is associated with the test statistic if that Z value is greater than the critical value. Then you should reject the null hypothesis because it’s in the rejection region. If the Z value let’s say by the way, this is the mean, let’s say if the Z value is not in a shaded region, Then you should not reject the null hypothesis. You should keep it now. I’m gonna talk about how to get those Z values in another video, but for now let’s talk about the other one tailed test. There’s two of them. So the first one would be a left-tailed test and the second one is a right-tailed test. Both of these are one-tailed tests now at a 95% confidence level alpha will still be point zero five, so for the left tailed tests, alpha is going to be completely on the left side now. This is when he’s supposed to use an left tailed test. Let’s say that the alternative hypothesis is that the mean is less than 100 so if it’s less than some number, you need to use the left tailed test. Now let’s say for the alternative hypothesis that the mean is greater than some number in that case. And then you would use the right tailed test. So that’s how you can tell whether you have a one tailed test or a two-tailed test. You need to look at what statement is made by the alternative hypothesis. If it doesn’t equal a number, then your calculator. Z values can be on the left side or on the right side, so we need to use a two-tailed tests. If you believe that the mean is less than a number, then your calculator. Z value is gonna be somewhere on the left side of the mean. So you need to use a left tailed test. If you believe the mean is greater than 100 then likely your calculated. Z Value is going to be on the right side of the mean, so you need to use a right tailed test. So that’s how you know which type of tests you need to use. So that’s it for this video. Thanks for watching and don’t forget to subscribe.

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