Challenge activity 431 confidence intervals for population...

challenge activity 4.3.1: Confidence intervals for population proportions. Critical values for quick reference during this activity. Confidence levelCritical value 677446.4308986.qx3zqy7 In a poll of 1000 randomly selected voters in a local election, 767 voters were against fire department bond measures. What is the sample proportion ? What is the margin of error for the confidence level?

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00:01 Hey there, welcome to numerate.

00:02 We were actually constructing 99 % confidence interval over here for the population proportion.

00:12 So let's first write what we're given here.

00:15 So we're given the sample size and the x value.

00:21 So what we are trying to look here is p, right? so p is the proportion, so we're going to do 169, divided by 1 ,000.

00:30 And we're going to get a value of around 0 .169 for p.

00:44 And with that, we also need to find our z critical.

00:48 Based on a 99 % confidence interval, it will equal around 2 .58.

00:55 And again, our sample size is the 1 ,000.

00:59 So let's calculate this.

01:01 Put into our equation first.

01:03 So we will have confidence interval equals.

01:18 We draw this here.

01:21 Okay, equals.

01:22 So our proportion here, let's just round up to 0 .17, but we're going to carry out of digits when calculating, plus and minus our z critical, 2 .58 times the square root.

01:42 So what we have is 0 .17, so 0 .17 .1 .1 .1 .1 will equals 0 .83 divided by 1 ,000.

01:55 Okay, so we're going to get a lower bound and upper bound for a confidence interval.

02:02 Let's see here...

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