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Ifn-10, z(x-bar)-36, and s-9, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population:Give your answe...

Question

Ifn-10, z(x-bar)-36, and s-9, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population:Give your answers to one decimal place.pGet help: VideoBox 1: Enter your answer as an integer or decimal number: Examples: 3,-4,5.5172 Enter DNE for Does Not Exist; 00 for InfinityBox 2: Enter your answer as an integer or decimal number: Examples: 3, -4,5.5172 Enter DNE for Does Not Exist; 00 for Infinity

Ifn-10, z(x-bar)-36, and s-9, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population: Give your answers to one decimal place. p Get help: Video Box 1: Enter your answer as an integer or decimal number: Examples: 3,-4,5.5172 Enter DNE for Does Not Exist; 00 for Infinity Box 2: Enter your answer as an integer or decimal number: Examples: 3, -4,5.5172 Enter DNE for Does Not Exist; 00 for Infinity



Answers

Construct a confidence interval of the population proportion at the given level of confidence. $x=80, n=200,98 \%$ confidence

Playful A trials and e equals 1100 trials we observe are 860 times from this. We want to answer the following question related to constructing a confidence interval for population proportion. People. We proceeded the four steps listed below to solve this problem first, we need to find the point estimate of PP had pizza is simply are over end, which is .782. Next, what we need to do is determine whether or not we can actually construct this confidence confidence interval. We need to check the requirements. This is the fact that mp tens one minus P is greater than equal to 10. This is 100 87. So yes, the requirement is met. Next we construct the interval so the intervals P minus E where E s Z score times one, let's be over end for alpha equals 10.94 94%. Z is 1.88 which means plugging in. We have equal 0.23 and the confidence interval is 0.7592 point 805 which we can interpret to mean that were 94% confident. The population proportion is between 940.79 point 805

To find a 94% confidence interval for the population proportion. We want to recall that confidence intervals for population proportions are formed by taking the P hat point estimate for the population proportion minus e. The margin of error to p hat, the point estimate of the population proportion plus e. The margin of error. So you get your lower bound frumpy hat minus E and your upper bound from P hat plus eight. Where P hat is found by taking X. The number in your sample that had a specific characteristic that you're focusing on divided by N and E is found by taking Ziese of alpha over to the critical value from the standard normal distribution associated with your specific level of confidence times the square root of P hat times one minus P hat divided by And so here our P hat is going to be Our X which is 860 for this problem divided by and Which is the 1100 from this problem. So that gives us a p hat of 0.782. And we usually like to run these 23 decimal places now. What about E? Well for e we know p hat we know n. The thing that we need to talk about is how do you find this Z visa alpha over to value? Well for Z sub alpha over to you need to find the critical value associated with the specific level of confidence. So we start by taking and drawing a standard normal curve and recalling for a confidence interval, it is equally spaced Um on either side of the middle of the distribution. So that's where your .94 Area of the distribution is and this is .94 again because it was a 94% confidence interval. Now the entire area under the curve is one Subtracting the .94 Is going to give us a 0.06 and that's the alpha. That's the area. In the combined two tails and Alpha over two is how much area is in each individual tail. So dividing 20.6 by two gives me a 20.3 which is in each individual tail. Those are the areas, but your critical value is the Z score cut off. That would segment this distribution at that vertical line. So it has an area that's to the left of that cut off, going Not only the .94, but also the .03. So .97 is the amount of area that's to the left of that cut off when we want to find this disease of alpha over to. Now we can find this by looking it up backwards on a normal distribution table. Or if you have a calculator or even search online for inverse norm. But yeah, Most generally the first thing you enter is the area to the left of that. Cut off that .97 comma the mean of the Z scores is zero and the standard deviation of the Z scores is one. And when you go through that calculation you will get uh Z sub alpha over to critical value for a 94% confidence interval is 1.881 rounded to three decimal places. So that value is what goes in your piece of alpha over two. So now my E Is equal to the 1.881 times the square root of our 0.782 times 1 -0.782. Yeah, And that divided by our end, which is the 1100. Now calculating that and rounding it to three dozen places we get E. is equal to 0.023 for our lower bound. Then it's P hat minus E. So 0.78 to minus the 0.23 For lower bound to our p hat 0.782 Plus the 0.0234 hour upper bound, Carrying out the calculations you'll get 0.759 for lower bound to 0.8054 upper bound. And often they will write this as a Um open interval. So they'll usually write this as the interval between 0.759-0.805. Now if you have any questions about how the critical value was found if that's what's getting you stuck be sure to go back and review the videos on finding the critical values. The sub alpha over to Yeah.

Here in this problem. First time calculating the value of P as we know that P is equal to x y n So just putting the value which are given in the question 1 20 by 500 on calculus and I get 0.24 now the confidence level interval can be calculated by the formula. So here we have to calculate the 99% confidence interval of the population proportion. So it is given by the Formula People's Zad al far by two multiplication under the P multiplication one minus p by end going forward and simplifying it further so on putting the value I can write the Christian edge 0.24 plus minus 2.5 paid multiplication under hood, 0.24 multiplication and 0.76 by 500. Now on solving it, I get the final answer for this problem. So I get to values which I am writing here 0.191 as well as 0.289 So both are the answer for this problem. I hope you understand the solution

You were asked to use a computer calculator to construct a confidence interval of 98% with the sample data given to us, which is gonna be 67 12 mine. 10 8 59796 So how even do that is go to excel and enter are sample data there into a columns to make sure it's going downwards so you would enter in your cells. Let's say you're starting a A. One would be six. A two would be seven. A three would be 12 and so on and so forth. So once you have that column solidified, you're gonna go into your mini tab and then you would select stat, and then you would go to basic statistics. And then you would click with one sample T because we have just one set of data that we're looking at. So then you would in the samples in columns, you would select whatever you put your columns. And so let's say it was just a so a one. Make sure that it's clicked and then you would go to your options, and then you would put in your confidence interval for a confidence level of 98.0. And then you also just need to make sure that the alternative is set Teoh not equal. So I'll give you the correct output. So once you have all that, all your data is in there. You can click, OK? And you give you something that looks like this. So it should be one sample t and then whatever calling you wouldn't. So let's say a one you shoes day, it'll spit out the output that looks kind of like that. So at the top of the your variable your en your mean your standard deviation your sample mean in the 98% confidence interval so that it'll show what column used for her very most. How many which is calculating of 12 the mean, which is also calculated, the standard deviation which they calculated the sample standard of Asia. And then our confidence interval right here, which is what we want, shows us 6.73 to 9.4 27 So the answer for that is 98% of our data is gonna fall between the range of 6.73 and nine point for juice


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