If we use the information from the first sample, we would estimate the population proportion with \(\hat p_1 = \frac\].And then, you could use both samples individually to estimate such population proportion. Thanks for watching! We’ll see you in the next video.The idea of a pooled proportion is the following: Say we have sample information from the populations that have the same proportion. And if your stats teacher is boring or just doesn't want to help you learn stats, go to, where you can learn more about accessing our lecture videos or provide feedback on what you’d like to see. Be sure to leave your comments below and let us know how good a job we did or how we can improve. Nice work!Īnd that's how we do it at Aspire Mountain Academy. So we going to say, “No, you shouldn't just simply survey the adults of the nearest college because it's a convenience sample.” So we look at our answer options and find the one that corresponds with that. And of course, convenience samples are biased samples, so we don't want to be sampling with that methodology. Nice work!Īnd now the last part, Part C, asks, “Given that the required sample size is relatively small, could he simply survey the adults at the nearest college?” Well, what kind of sample do you have when you sample what's nearby? I hope you said, “A convenience sample,” because that's what we've got. So we’re just going to round up to the next nearest integer to give us 76. We crunch those out of our calculator, and we get 75 with a bunch of decimals behind it. And now we’ve got new numbers to put into our equation. So we’ll just subtract 0.79 from 1 to get 0.21. We want to be - a survey suggests that 79% of adults of brand, so that's our proportion of success, which then means the proportion of failures is going to be the complement of that. The only thing that changes are values for p-hat and q-hat. And we still want to be within six percentage points of the true population percentage, so this value for E doesn’t change. We’re still 80% confident of the estimate, so our critical value doesn't change. So I’m going to go back here and start over with my original equation for determining sample size, and now I plug in new values. We can easily repeat the calculation with the new numbers. Now the second part, Part B, asks that we repeat the calculation, but now we are going to assume that 79% of adults have heard the brand. That gives us 114, so I put that here in my answer field. Since we can’t really count partial people - we’re only counting whole people - we’re going to round up to the nearest integer. We’re asked to round up to the nearest integer so we get this partial person counted for. We get 113.7 and the seven is repeated off into infinity. Now that I've got my numbers substituted into my equation, all I need to do now is just calculate that out. So notice how we write that here - 6%, six percentage points of the true population percentage. And then we want to be within six percentage points. In that case, the most conservative percentage that we can collect for p-hat is going to be one half, which then means q-hat is also one half. We don't know anything about the percentage of adults who part of the brand. Alpha over two says we want to split alpha amongst the two tails of our distribution. This is where we know it's a two-tailed area - z-alpha-over-2. So 1.28 was the critical value we just found. Here's my equation for sample size, and I just substitute in what I have. Now that I’ve found the critical value, I can actually substitute into my equation. There are my two critical values I really only need the positive one (1.28), so that's what I'm going to use. And then here in the percentage, I’m just going to put in I want 80% confidence. So then I want the two-tailed critical value, so I’m going to click the Between option. And we want the standard Normal distribution that's the default here in the Normal calculator. I’m going to pull up the Normal calculator. I could also do this with the z-score tables, but I'm just going to use StatCrunch since it's my preference. To do that, I’m going to open up StatCrunch so I can access the calculator inside StatCrunch. So the first step we’re going to have to take to calculate the sample size that we need is to find the critical value. OK, Part A says we should assume that nothing is known about the percentage of adults who heard the brand.
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