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A. Let p be the population mean: Determine the null hypothesis, Ho, and the alternative hypothesis, Ht .Ho: p = H,: p#...

Question

A. Let p be the population mean: Determine the null hypothesis, Ho, and the alternative hypothesis, Ht .Ho: p = H,: p#

a. Let p be the population mean: Determine the null hypothesis, Ho, and the alternative hypothesis, Ht . Ho: p = H,: p#



Answers

Consider a hypothesis test for two population proportions with the null hypothesis $H_{0}: p_{1}=p_{2} .$ What parameter is being estimated by the a. sample proportion $\hat{p}_{1} ?$ b. sample proportion $\hat{p}_{2} ?$ c. pooled sample proportion $\hat{p}_{\mathrm{p}} ?$

When you take a sample or samples, those samples are used to estimate your population proportions. So when you have when you get an uh sample proportion from group one, that's going to estimate the population proportion. Mhm. From your first population or from your first group. Mhm. Yeah. And then your, he had to estimates the population proportion of group two or your second population. And then PLP is your your pooled sample proportion or combining your two P. Hats together. Which is going to estimate the combined population proportion of both groups? You should go. Mhm.

So when doing hypothesis tests, we're going to have a null hypothesis or a hope and an alternative hypothesis or ha when we're looking at part A Were asked if the population mean is more than 10 and we're going to connect a hypothesis test to find that out, um When we start our hypothesis test out, we're going to assume that the population mean you Is going to be equal to 10. But then for alternative hypothesis which we're trying to show evidence for is that it's greater than 10, so mu is going to be greater than 10. That's gonna be for part A. Now for part B We're asked to find some evidence that the population mean is not equal to seven. So our hypothesis or in all hypothesis would be that our population mean is seven and the way we would write that the population mean isn't seven for alternative hypothesis would simply be mu Does not equal seven like this. And then for part C we're going to try to provide evidence that the population mean is less than five. So we're going to assume that it is five as are null hypothesis. Yeah. And or alternative will be that it is less than five. Yeah.

I have to determine a few null and alternative hypotheses in this question. The first which says the variances of populations A and B are not equal. What is going to be my null hypothesis for this? It is going to be that both of them are equal and the alternative is going to be that both of them are not equal. The be part says the standard deviation of population one is larger than the standard deviation of population to in order to get the standard deviation in order to check for standard deviations. Also, I can just square them and get the variances, and I can check the hypotheses for variances. When I square them, I get Sigma One square and sigma to square and my age not is going to be that both of them are equal. And my alternative hypothesis is going to be that Sigma Square for population one is greater than the sigma squared for population to and whatever result I get for variances is also going to hold for the standard deviation. Now the C part. The sea park says that the ratio of the variances for populations A and B is different from one. So again, my name is that they are equal to one. The issue is equal to one, and the alternative is that it is not equal to one. What is the deeper the deep part says that I have tow, you know, check the variability within the population, see if it is less than the variability within population deep. So what I have I've just said that the issue of their variances is equal to one. This is my null hypothesis and I'm checking if the ratio of the variances off d two C is greater than one. So this is my melon alternative for this case over here, C or D whatever is in the numerator denominator for the null hypothesis does not matter. So let me put D in the numerator and seeing the denominator. So these are my null and alternative hypotheses.

In this question. Also, I have to stay the null and the alternative hypotheses for a few cases. Let's go to Casey. What is a C? He says that the standard deviation of Population X is smaller than the standard deviation of population. Why? So I have standard deviation off population eggs. So what I can do is I can simply find the variance by squaring it and the center division of population. Why again? I find the variance Manal hypothesis is that both of them are equal. So this is equal to one, and my alternative will be X is smaller than why that this thing over here Sigma X squared upon Sigma Phi squared is less than one. Or I can even say that sigma white square upon Sigma X Square because this is actually thought to be easier to find. So sigma by square upon Sigma X squared is greater. This is greater than one. Let's go to the be part. What does the B but have to say? The be part says that the ratio of the variances off population a over B is greater than one again. Not like what this is is that I experience a severe Reince off eight upon variants of B. This is equal to one. And my alternative is what I'm trying to see. That is medians off A upon variants of me. This is greater than one. This is my null. This is my alternative. The C part The sea part says that the standard deviation of population Cuban is more than that off is at most that off, uh, population que do, Which means that the standard division off you too is greater than or equal to that off population Cuban. So again, let me write the variances. Sigma q two square upon Sigma Q one square. This is equal to one. This is my knowledge hypothesis, and my alternative will be that this fraction Sigma Q two square upon Sigma Q one square. This is greater than or equal to one. All right, what does it deeper? What does the deep part have to say? The variability within population one is more than the variability within population to again the Sigma square for population one upon sigma squared population to this is equal to one. This will be my null and my alternative will be that this ratio is greater than one. So I think that these are all the options here, and these are my answers.


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