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@r shecertpoln of 950 homeowners in the U.S , one In eight or she [S currently pzying off. homeowners reports having home equity Ioan that he What Is the 95% confi...

Question

@r shecertpoln of 950 homeowners in the U.S , one In eight or she [S currently pzying off. homeowners reports having home equity Ioan that he What Is the 95% confidence Interval?[0.1041,0.1459][0.0541.0.0959][0.1241,0.1759][0.1141.0.1559]

@r shecertpoln of 950 homeowners in the U.S , one In eight or she [S currently pzying off. homeowners reports having home equity Ioan that he What Is the 95% confidence Interval? [0.1041,0.1459] [0.0541.0.0959] [0.1241,0.1759] [0.1141.0.1559]



Answers

Home Ownership Rates The percentage rates of home ownership for 8 randomly selected states are listed below. Estimate the population variance and standard deviation for the percentage rate of home ownership with $99 \%$ confidence. Assume the variable is normally distributed. $$ 66.075 .8 \quad 70.9 \quad 73.9 \quad 63.4 \quad 68.5 \quad 73.3 \quad 65.9 $$

In this question, we are analyzing the housing market. The Realtors randomly sampled 36 bids from potential buyers to estimate the average lost in home value. The sample showed the average loss off 9560 with standard deviation off 1500. What assumptions and conditions must be checked before finding a confidence interval. Well, what are the assumptions when we find the confidence interval? The first one is Yeah. The first one is that they are normal. It was normal. And since the sample sizes bake, we can say that Yes. At this moment, the second one is a test off independence just off independence. What is exactly meant to buy the test off independence in the Yeah. What is wrong with the spending independence? The rest of independence means that the sample that you're taking from the population should be less than 10%. Meaning that if this is your population, the sample that you pick up should be less than 10%. Which means if I take this sample it is acceptable. But if I take this sample, it will not be acceptable. Why? Because the when I sample it again and again, let's say This is my first sample. This is my second. This is my third. There will be a novella hence it is considered that you know it should be less than 10%. This is one of the conditions. What was the third? Now? The three conditions first one is normal. Second one is independent and the third one is that off every class You should have more than 10 samples. So here there are no classes. So we're going to just take these two assumptions on both of these are satisfied. Okay, Now how do you find the confidence interval It is given by my mean confidence Interval is given by my mean plus or minus the critical devalue. What is the confidence interval that I have? It is 95% and my degree of freedom of 35. So critical value for 95% confidence interval and degree of freedom 35 that I'll put here multiplied by s by 10 s of the standard deviation that I have is by end. What is that? And is 36 in our case s s over here. We have 1500. What is the Mu Mu has given us 9560 And what is t critical? The critical for this case turns out to be 2.3 You can find it using a detail will. But yeah, a statistical software will do. And I think that he, for this value, comes out of the 2.3 piece and just input the values and the interval that you should get it. 9052.5 9052.5 to 10 6710067.5 This is my confidence. Interval Interpret this interval. What does what does this? A double show. It means that if I continue taking these samples in 95 percent off my samples or the confidence interval for 95% off my samples will contain the true population Will way our internal percent confident that the interval that we have got contains a true mean loss in value per home. These are answers

Following solution to # 18. And this looks at a study of home ownership. Uh and there's a study saying, okay, how many people own their homes with? You're a certain age? We're gonna use this formula. You can drive this using the margin of error formula. Or you can just use your book the same thing in the book, but it's P hat times one minus P hat times the critical value divided by the margin of air quantity squared and were given most of these things in the prompt. So it says that we want a margin of error to be 2% points. So the margin of error is going to point out to And then we want 90° confidence. Now, if you don't have 90° confident confidence, critical value memorized. First off, you should have at least a few of these memorized and it is 1.645 So you can get that from a table or you can use a calculator. I'm going to use a T. I 84. And if you go to second distribution and you go to inverse norm And you just change that area 2.9 for the 90%. The mean is zero. The standard deviations one and then for confidence intervals is always a thinner tail. Now this is a newer calculator. If you have an older calculator, you actually have to put in It's a little bit different but it's all for over two. So you have to put in .5 and change it to left or right. Um and then we paste and then this is going to give us the critical value. Now this one gives you two critical values but it's just the absolute value of it. So it's 1.645. That's where I get that. And then the p hat is also given. So from a previous study, 67.5% of them on a home. So .675 and then 1- that would be .3-5. The 1 -175.3- five. So then I'm going to use the formula. So I take P. Hat which is .67 five times one minus P hat 10.3 to 5 Times the critical value 1.645 Divided by the margin of error of .2 quantity squared so you can use your calculator and plug that in. You may need to go in pieces but you carefully plug that in and you should get 14 84 0.1 And then we always always always round up. We never round off. Now we're always taught early on. Okay, that's 1484 buttons statistics. That's not the case. You always round up to a more conservative estimate. So 1485 Is the correct answer. So 1485 if we want a margin of error of 2% points. Now, whenever we have no prior estimates, we use the same formula but instead of p hat Of .675 and 1 -7 had is that we just use .5.5 for both. So this kind of maximizes the number that you need to sample. So the less, you know, that's typically what happens, the less you know, the more conservative you need to be Um in your estimates 2.5 times .5 is gonna maximize that result. And whenever you plug this in the calculator should get 1691 .3. So again we round that up to 1692. Okay. And another good check. Um whenever you have no prior estimates, the sample size will always be larger than if you actually have prior estimates. So 1692 is larger than that, 1485. So we know we did this.

Solving party first. As we all know, that Ziad Alfa by two is equal to 0.10 by two, according to the given data, which is equal to 0.5 which is equal to 1.645 As we all know that the sample size formula is given by any equal to p multiplication one minus p. Multiplication Jed Alfa by two by e It's square now I will just put the value here so I can write the question edge anything equal to zero point 669 Multiplication one minus 10.669 Multiplication 1.645 bye 0.2 square on simplifying. I get an equal to 14 98 now solving part B. So in part B, we have an equal 2.25 multiplication Ziad Al for buy to buy E square now just putting the value so I can write the equation as an equal 2.25 multiplication 1.645 by 0.2 squad and I'm solving. I get an equal to 1691 This is the answer for part B. I hope you understand both the solid

Problem. 11, we have a rate of 65.9% home ownership in the US We will choose a random sample of 120 households 120 to see the probability that 65 two 85 of them inclusive, live in homes that they own. First, this is a binomial distribution because it has discrete values, but we have a large sample size, which can be approximated to a normal distribution. Let's first check if it can be approximated to a normal distribution. We have two conditions and multiplied by B must be greater than or equals five. And then what? To blow it back. You is greater than or equals five b is a success rate and is given here. Then we have 120 multiplied by 65 point tonight, divided by 100. This is N B. Of course, it's greater than or equals five. This is a check, and we have multiplied by Q. But she is a compliment for the success rate, which is the failure rate. It's 100 minus 65.9, which is 34.1, divided by 100 and Of course it's greater than five and it's already chilled. Which means we can know state a random variable X, which follows a normal distribution with new and set Were You equals nb and it's calculated here 120 multiplied by 0.659 This gives 79.8 and Sigma equals square root. N PQ equals square root of 120 multiplied by 0.659 are deployed by Q, which is Oh boy, 341 These gifts five 0.193 Now we want to find the probability that the random variable law is between 65 and 85 inclusive and then And so I have added the equal sign here and here. What is this probability? We can rewrite it as it equals the probability for ex being smaller than 85 minus the probability for X being great smaller than 65. It's imagine the normal distribution. We want to get the area between 65 68 the 85 65 85. We want to get this area, Then we can get the area to the left of 85 minus the area to the left of 65 and we will make a correction for it. It's the probability for ex smaller than 85.5, because here we have an equal sign smaller than equal. Then we will add 4.5 to the value of X here, minus the probability for X smaller than 65.5. This is a correction from the binomial to the normal distribution. The fourth step is to get does that value for the school which corresponds to each of them. Let's make this that one equals 85.5 minus mu. New is defined in step two, 79.9. Buy into it 79.8 divided by sigma, which is calculated as 5.193 Then they'd want equals 1.2 three or 1.24 and we can get the U. S. 65.5 minus mule divided by sigma, which he gives minus 2.62 By entering the standard normal distribution tables, we can get the area do that if of that one which represents this probability minus and they get to the area to the left of the two, which represents this Probably let's enter the tables was that one equals 1.24 1.24 here, 1.2 and four is here. Then this is the probability to the left of 1.24 4.89 to 51 Then the probability for ex being greater than 65 smaller than 85 inclusive equals 4.89 to 51 minus. Let's enter the tables again to get the area to the left of minus 2.62 minus 2.62 2.6 year, 2.62 Here it's all point Oh, 44 Oh, 44 Then the probability is four point it, Yeah, 811 And this is the final answer of our problems.


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