Degrees of Freedom For Example 1, we used df=smaller of n1-1 a...

Question

Degrees of Freedom For Example 1, we used df=smaller of n1-1 and n2-1 we got df=11 and the corresponding critical value is t=-1.796 (found from Table A-4). If we calculate df using Formula 9-1, we get df=19.370 and the corresponding critical value is t=-1.727 How is using the critical value of t=-1.796 “more conservative” than using the critical value of t=-1.727

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Suppose you are conducting a 2 sample T test and have 2 sample sizes. N1 equals 10 and N2 equals 15. Using the conservative approach, you use degrees of freedom equal to the minimum of N1 minus 1 and N2 minus 1, which is 9. This gives a critical value of T equals 2.262 for a one tail test at the 0.05 significance level. If you instead use the formula for degrees of freedom and get 17.8, the critical value is T equals 1.740. Y is using T equals 2.262 considered more conservative than T equals 1.740? Awesome. So it appears for this particular problem, we're asked to determine why is using T equals 2.262, considered to be more conservative than T equals 1.740. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is because a larger critical value requires stronger evidence to reject the null hypothesis. B because a smaller critical value makes it easier to reject the null hypothesis. C because it increases the probability of a type 1 error, and D because it uses more information from both samples. Awesome. So first off, in order to solve this particular problem, we need to recall that a more conservative test means that it will be harder to reject the null hypothesis, which will therefore help reduce the chance of a type 1 error occurring or from a type 1 error to occur. Secondly, the critical value of T, so if we take a critical value of T is equal to 2.262, and once again, as you should recall a note, the critical value T equals 2.262 with degrees of freedom of 9, which I'll put in quotation marks, is farther from zero than. T equals 1.740 with the degrees of freedom 17.8. So thirdly, as we should recall and note, a larger critical value means that the observed test statistic must be more extreme in order to reject the null hypothesis. So therefore, as a result, as we should recall, when using T equals 2.262, Is a more conservative value because it sets a stricter threshold for significance, which makes it less likely to reject the null hypothesis by chance. So that will mean, without a doubt, our final answer has. To be multiple choice answer letter A, which is once again because a larger critical value requires stronger evidence to reject the null hypothesis. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Degrees of Freedom

Critical Value

Conservativeness in Statistical Testing

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