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14. For the each of the null and alternative hypothesis below; determine ifit represents valid null and alternative hypothesis Ifthe null or alternative hypothesis ...

Question

14. For the each of the null and alternative hypothesis below; determine ifit represents valid null and alternative hypothesis Ifthe null or alternative hypothesis is not valid, explain why: Ho: L = 20 valId Ho: p # 18 Ha: p 2 20 Ha: L =18 QeFid Ho: p =0 vdlid Ho: > = 15 Ha; | < 0 Ha; > > 15 Vald Ho: 0 = 20 VBFa Ho: p =5 valid Ha: p > 19 Ha; p > 5 Ho: p < 0.20 nt Ho: p = % Valid Ha: p > 0.20 valid Ha: p z V

14. For the each of the null and alternative hypothesis below; determine ifit represents valid null and alternative hypothesis Ifthe null or alternative hypothesis is not valid, explain why: Ho: L = 20 valId Ho: p # 18 Ha: p 2 20 Ha: L =18 QeFid Ho: p =0 vdlid Ho: > = 15 Ha; | < 0 Ha; > > 15 Vald Ho: 0 = 20 VBFa Ho: p =5 valid Ha: p > 19 Ha; p > 5 Ho: p < 0.20 nt Ho: p = % Valid Ha: p > 0.20 valid Ha: p z V



Answers

A null and alternative hypothesis is given. Determine whether the hypothesis test is left-tailed, right-tailed, or two tailed. What parameter is being tested? $$\begin{aligned}&H_{0}: p=0.76\\&H_{1}: p>0.76\end{aligned}$$

In in this question we want to determine whether the given hypothesis test is left right or to tear. And then we want to evaluate what parameters being tested. We have no hypothesis. H. And R. P equals 0.2 alternative hypothesis H. A. P less than zero point to this question is channel. Do you understand the other way with the hypothesis tested? In order to answer whether or not this test is left to right or two tails. We determine what the definition of each type of test is. The same protesters follows for right tail. The parameter is greater than an H. Not H. A. And left tail. The parameters less than an H. Not. And in a two tailed test is not equal to the agent parameter. Since Rhhs P less than 20.2, it's clear that our test is therefore left tails. Next to conclude what type of parameters being tested. We simply have to know this is the proper terminology or more simply the symbolism of P. So for this we have our solution the parameter being tested as P. Which is the population proportion.

Oh researchers conducted hypothesis tests for population proportion P with no hypothesis H. Not that the population proportion is 0.65 An alternative they want to test for P does not equal 0.65 or differs in either way. Hence, a two tailed test for this test, they obtain a p value of 20.0 to explain what this p value represents and whether or not we can make a conclusion with regard to the test from this P value alone. To start off with that's one of the p value, 10.2 corresponds to a probability of 0.2 out of one total, that we would observe sample data as extreme or more extreme than we did. And since it's a two tailed test specifically, we have that the probability of finding the extremists that data is 20.1 or other 0.1 on each end of the distribution and some 2.0 to do symmetry a 0.2 P value is fairly well, since we only reject H not one P is the alpha, and alpha is usually something like 10.1 point 5.1 These results are in fact statistically significant, so alpha is less than 2.0 to that is if we have an alpha value less than equal 2.2 we can reject H not there. So for a 0.1 point 05 we can do so, however, for an alpha value lower like 50.1 These results statistically insignificant, and we won't be able to reject h f.

Now This time we have another hypothesis as please equal to 0.76 p is equal to 0.76 And our alternative hypothesis at speeds greater than 0.76 p is greater than 0.76 Now, what is the population parameter that is being tested here? P is proportional. So we're checking the population proportion, the population proportion. Now, over here, if we look at this, we have the null hypothesis as P is equal to 0.76 and the alternative is P is greater than 0.76 So if this is my normal distribution greater than means, I'm going to look at the right hand side, right? This is going to be my deduction region. I want to see if my proportion is significantly greater than the claimed proportion of 0.76 This will be around 0.76 The mean right. So this is going to be a right tail test. This is a right detailed test

We have a hypothesis test with P values 0.083 for are observed data. We want to determine for each of the alphas or the significance values below whether or not our P value enables us to reject the null hypothesis each not before getting started. Let's remember a critical definition. You can reject the null hypothesis, H not whenever P is less than or equal to alpha. So whenever your P value is less than or equal to your significance level. Now implementing this in part A We have that 0.083 is greater than alpha equals 0.05. That means that P is greater than alpha. So for part a we do not reject the null hypothesis. For part B, alpha equals 0.1, 0.083 is less than or equal to 0.1. So in this case P is less than or equal to alpha. And we were able to reject the null hypothesis. Finally, for part C 0.083 is actually greater than the alpha value here of 0.06. So again P is greater than a, and once again we do not reject the null hypothesis.


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