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6) Use this scenario for the next two questions: You wanted to understand the proportion of dogs who wear their tags regularly: You study 400 dogs and found that 30...

Question

6) Use this scenario for the next two questions: You wanted to understand the proportion of dogs who wear their tags regularly: You study 400 dogs and found that 304 wear their tags regularly:a) For this study, what will be the standard deviation of the proportion of dogs who wear their tags?(Provide work in the final upload)Your answerb) What will be the margin of error for a 84% confidence interval for this study? (Provide work in the final upload)Your answer

6) Use this scenario for the next two questions: You wanted to understand the proportion of dogs who wear their tags regularly: You study 400 dogs and found that 304 wear their tags regularly: a) For this study, what will be the standard deviation of the proportion of dogs who wear their tags?(Provide work in the final upload) Your answer b) What will be the margin of error for a 84% confidence interval for this study? (Provide work in the final upload) Your answer



Answers

Use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval. From a KRC Research poll in which respondents were asked if they felt vulnerable to identify theft: $n = 1002 , x = 531$ who said “yes.” Use a $95\%$ confidence level.

Hello. Welcome to this lesson. In this lesson. We have the following data. Yeah. And would find for the first part the bestest meat for the population proportion people. So the one is the the number that chose the window seat That is 492 all over. The total. Which is 806. Yeah. So we have the estimate yeah. As 492 Divided by 806. So that is 0.6 10 for Or 61 point. There are 4%. Okay. Dennis padre is to estimate the martin of error. With this one will be looking for the Critical Valley α on two times the p the script of a p times one minus the P. Q. All over. And the size. So here we look at enough of that is zero so 1 1% all over to. So this would become 0.0 05. Now The 0.005 minutes that we are looking at an area which stretched at 99.5% to the left. So 0.005 from the table. You are looking at 99.5%. So 99 5% is here. And that is 2.5 Then plus 0.08 from this side. two can fire from that. So in total we have 0.5 Then plus 0.08 which is he called to 2.58. All right. The arrow now becomes 2.58 than 0.6. 0.6104. Yeah. Then 1 -0.6104 Over the end which is 806. The margin of error now becomes Mhm Yeah. Yeah. 0.0443. Now the c pad would construct the confidence interval of the population proportion. So we have minus E. The proportion lies in this interval. And now that is 0.6104 -0.0443. Oh 0.61204 plus 0.443. Oh wait so on the left We have zero on 5 661. Mhm. No the right. Oh we have zero .654 seven. Okay. So this brings us to the last part, the deeper where we would interpret what we have here and that is we are confident We are 99% confident. Oh yeah that's the proportion we found the proportion. Yes. Within. Yeah. Gerald .5661 and 0.6 547. Alright, sometimes for a time this is the end of the lesson

Mhm. Okay. This question were given the end 725 and X musical 275. It's so cute simply X summer. And Just to 75-85, Let's get this year 35 mm he said of moving to value. Mhm. For the 95 confidences Is 1.96. Get everything. Okay. Okay. And the 95% confidence interval about the population proportion of adults follow college football and then be given in this general over the people. That's what is? I don't have to discouraged. He persecute from the peak. Okay. Right. Which would give us Europe 3 5 Less than -1.96 spirit. You have been 35 times 655 over. And which is given to the 75? Yeah, That's 0.317. What's your .383? It's a buster miners.

Mhm. Yeah, we're going to be calculating some margin of errors in this problem. And then looking at the relationship between sample size and margin of error for the first one we want 95% confidence interval. So my Z is going to be 1.96 tells us the standard deviation is four and the I'm sorry, 10. And the sample size is four. And when you multiply 1.96 times 10 over to you will get a margin of error of 9.8. Then in part B, it wants still 95% confidence standard deviation 10. But now our sample sizes 16, our sample size has been quadrupled. And when we multiply 1.96 times 10/4, we're going to get a margin of error of 4.9. So for the third question, you have to realize that this margin of error got cut in half when we quadrupled the sample size. So that would lead me to believe that in letters. See when I quadruple the 16 into a 64 I shouldn't really have to do any calculations here. I quadrupled the sample size so I'm gonna cut four point 9.5 and 4.9 cut in half is 2.45 And you could verify that that if you wanted, just by doing 1.96 times 10/8, and you would get 2.45

Especially given them and okay. There's 300 X. is 35. Mhm. P. X. She was 35. 200 A zero plant. Yeah. 11 son. I was I felt material value. Yeah. Mhm. For the 99% companies word on the street is okay. 2.5 everybody. Let's get And the 99% confidence interval about the population proportion of employed individuals who work at home at least once per week. Given by that's a minus said alpha two and of the deep And giving a 0.117 -2.58 times The square. It was your 117 I reserved .883. But there yeah, I think you better get it. Yeah. 0 69. You're 16.


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