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Out of 500 people sampled 230 preferred Candidate A_ Based on this estimate what proportion (as decimal) of the voting population (p) prefers Candidate A?Compute 95...

Question

Out of 500 people sampled 230 preferred Candidate A_ Based on this estimate what proportion (as decimal) of the voting population (p) prefers Candidate A?Compute 953: confidence level, and give your answers to decimal placesQuestion Help:VideoVOxE) VOTE

Out of 500 people sampled 230 preferred Candidate A_ Based on this estimate what proportion (as decimal) of the voting population (p) prefers Candidate A? Compute 953: confidence level, and give your answers to decimal places Question Help: Video VOxE) VOTE



Answers

Find the percent. Round to the nearest whole percent. $-292$ people in favor out of 450 people surveyed

If the votes are in a 7 to 5 ratio in favor of painted today, that means that Candidate A is going to get seven out of every 12 votes because seven plus five is 12 now. If 24,000 people voted, then you would expect candidate get how many boats well, cross, multiply and divide, and you will see that you will be expected to get 14,000 votes. But it says she only got 13 187 and so that would be less been expected.

All right. This question gives us some polling information and wants us to compute the margin of error. So part, eh just wants the margin of error from this sample. So remember that for a proportion, margin of error equals our special Z score times P Hat Times Q hat all over end, which in this case, we're dealing with 95% confidence soar. Special Values 1.96 and P hat and Q hat are both 0.5. And from here we get a margin of error of 0.0 for 42 Now we move on two to them, asking for different margins of error and us competing this sample size. So, for the first example at once margin of error to the equal to 0.4 So we'll use the following equation and all these examples and equals P hat times Q. Hat times The Z score over e quantity squared, which in this case the only thing that's going to change is our margin of error. So it's going to be 0.5 times 0.5 times 1.96 squared over e squared, which weaken group. The point fives together to simplify it, so it looks neater. So all we need to dio is insert are different values of e into this equation. So our first values 0.4 So 0.5 squared times 1.96 squared over 0.4 squared equals and which is 600.25 And for sample size questions with margin of error, we always round up because if we round down, our margin of error would not be small enough. And no, we just repeat the calculation with the different margins of air. So the next nest example it wants is 0.3 So we already have our equation, and now we just plug in point all three. And this time this works out to be, if 1067 0.1, which we round up 10 68 then getting smaller this time our margin of error. His 0.2 So we just plug in point or two for e, and this, for once, actually lands on a whole number 24 point 24 01 no decimal point. Then, for our final answer, our final part of this question Rather it wants a margin of error of 0.1 So using our Formula One last time, this time plugging in 0.1 And this works out to be another hole number 96 04 So, as you can see, decreasing our margin of error keeps making the sample size required going up and up and up. So that's the trade off if you want a smaller, more accurate poll with a small margin where that is.

Hi, everyone, start about problem 1 66 So let's start obviously apart. A We're gonna talk about what our population parameter is. So the question we're trying to answer is if this political candidate won the office he ran for So we're we're giving a sample size of 150 voters, and in that sample size, 35 of the voters voted for him. So these are the 35 voters from our sample that voted for a candidate. But what we need is we need how many people voted for him in the entire election, not just R 1 50 sample size. So what we are trying to determine is the percentage of voters that voted for our candidate here. So that's the answer to part A. Is the population parameter you're trying to determine is how the percentage of people that voted for a candidate So that's pretty. Let's go party over here. So this circle I just drew out is now he 150 samples eyes in this little wedge. It's the 35 people that voted for him. So the sample so is a statistic is like an average or ah percentage or some type of value, right? So what we're looking for again from part A. We're looking for the percentage of voters that voted for a candidate. So we know how many people voted for him from our sample, which is 1 50 by the way. And we have the sample size, which is 150. So all we need to do to find our statistic So percentage of voters it's just 35. Sorry, let's do it over here. 35 divided by 1 50 which will go out. I'll just go ahead and turn it into a percentage. It is 23.3% repeat it with a with the three repeating. So that's the answer party. There's a party is the value of the sample statistic were using, which is the percentage of voters inter sample that voted for our candidate IHS 23.3 repeating percent. So remember, this is only for our sample. It's not for the entire population, for all we know. Ah, our sample of 150 people could be a complete out liar, but it can. It's a pretty good guess, because we have a relatively large sample size. So, for see, the simple answer is no. You would not believe that a candidate that only got 23% of the vote would win an election. Ah, but he seems to think he wants. So maybe maybe our sample waas and out. Liar. But anyways, thank you for watching. And I hope this video helped you.

Okay, part a says a poll of 150 voters shows that candidate Is preferred by 5% of voters while 44%% prefer the opponent. So let's do a little bit of math here to see if the candidate should be concerned. First off we should probably look at the margin of error which is one over the square root of five plus or minus square end One over plus or minus. The square root of 150 C Square root of 250 is approximately 12.25. convert this to a decimal one divided by 12.25 is That's our -0.08 which is the same thing as plus or minus. Um 8%. So first up with this small sample size the margin of error is 8%. That's really large margin when it comes to elections. Second this candidate is preferred by 5% of the voters while 44% prefer the opponent. What's 5% of 150? Let's see. So 5%. 150. Yeah. So that means 7.5 people of 150 said that they like this candidate, you know, which is 5% obviously. So plus your mind is 8%. The most people that are going to vote for him are 13% And the fewest that are going to vote for him are 0%. You know this sounds very dire but you have to think about how many voters are there total Right now this is representing less than half of those 150 voters. So there's Another 51 people who haven't even responded or are voting for a third person. I don't think he should be concerned, but it's not comfortable for sure. Another poll about 600 voters shows up the candidates preferred by 55%. So let's take a look at the margin of error. First to take a measure of this. So one over plus or minus squared of 1600 squared of 600 is approximately 24.49, convert it to decimal. You're a point 04 one. So plus or -4.1%. This candidate should feel very comfortable now because even if we take away this version of error from his percentage, he still is going to get the majority of the vote Because 55% -4%. 51%. Sorry, His confidence interval is 51% to 59%. Well thought for him. So I think he should fuel where is she more confident at least a lot more confident than version A um, so just kind of summarizing my answer here pills concerned. Okay,


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