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For this problem; use the n-Im? formula.political candidate has asked you to conduct a poll to determine what percentage of people support her:If the candidate want...

Question

For this problem; use the n-Im? formula.political candidate has asked you to conduct a poll to determine what percentage of people support her:If the candidate wants only a 6.5% margin of error at a 95% confidence level, what size of sample is needed?Give your answer in whole people:Question Help: 0 Post to forumSubmit Question

For this problem; use the n-Im? formula. political candidate has asked you to conduct a poll to determine what percentage of people support her: If the candidate wants only a 6.5% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people: Question Help: 0 Post to forum Submit Question



Answers

Find the sample size needed to estimate the percentage of Republicans among registered voters in California. Use a 0.03 margin of error, use a confidence level of 90%, and assume that p ^ and q ^ are unknown.

Figure out what kind of confidence interval we're looking at in the study that interviewed 1015 adults, had a standard error of 3% and found that 68% of them believe in the specific political viewpoints. Now we're gonna take that The Z score is given by the standard error comes a square root of n over estimates for P and Q hat multiplied together. Our standard error is given by 3% point No. Three. Our end is given by the 1015 adults. R P is given by the 0.68 that agree with the leaning, and the Q is given by the rest of the 0.32 If you multiply all of that together, we got just about 2.5 and that's our Z score. And unfortunately, this doesn't line up with any of the standard ones that we've been looking at. So we're gonna have to go over to our table and find 2.5 by ourselves. Zoom in on the 2.0 row and the 0.5 column And where do they match up? Right here at 0.2 Okay, so 0.0, to what could we do with that? Well, what we're gonna do is we're first going to double it. Let's get points before and then we subtract it from one to get 0.96 0.96 If we convert that to a percentage, we get 96% and that tells us that this is a 96% confidence interval.

In 78 wants to know what would happen if we change the confidence interval to 95%. So he went from 90 to 95%. So if we increase our confidence level, our confidence interval will get wider. We're gonna be more confident. We got to include more numbers, so this gets larger. Are interval gets wider.

I want to construct in 98% confidence in trouble. Okay, Now 70% off The people said that they voted 70% means my peak up 0.7. So automatically, what is my cue camp? My cue. Careful. Become 0.3. I want to calculate a 98% confidence interval, which means my Alfa by two is 0.1 Okay, so if I calculate this critical value, this turns out to be 2.3263 So my Z Alfa by two is 2.3263 Okay, so what is the formula for E? It is the Alfa way, too multiplied by route over. Pick up Q capped by n All right. So let's use a calculator. This is route over 0.7, multiplied by 0.3. Divided by what is the sample size? The sample size is 1002 people. So n is equal to 1002. So this is development 1002 and this is multiplied by 2.32633263 So this is zero point 0336 My E is 0.3 367 Okay, now, how do I find a confidence interval for this? The confidence interval is going to be P is going to lie between 0.7 minus 0.3 three 67 on this is 66 6. 33. This is 0.66633 and the other thing is 0.7 plus 0.3367 This is 0.73367 0.73367 All right, now, this is our confidence interval. And the second question is asking other survey results consistent with the actual voter turnout of 61%. No, the actual voter turnout is less than this. Why? Because this does not fall in our interval. So we can definitely say that the actual turnout was less and this is going to be our answer

So 77 wants us to come to construct the 90% confidence. Terrible. So 0.65 plus or minus. So it's the 180th percent. So 1.645 times the square read of 0.65 times 0.3 thighs, all over 1200. So simplifying 0.65 plus or minus 0.23 So this is your air bound or your margin of air and then 0.6 to 7, 2.673 would be your confidence interval.


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