In the market for meat, in the absence of reputation,...

in the market for meat, in the absence of reputation, government certification, and other third-party verification, we would expect that people aren't willing to pay more for organic meat will pay less for standard meat and more for organic meat will only buy organic meat will only pay an average of the value of organic and standard meat

Transcript

00:01 So you are assuming that in 2014, 45 % of all american said that they actively tried to include organic foods into their diets.

00:12 Now, in a sample, considering 2 ,100 americans, they found that 1771 said that 171 said that they are always trying to include organic food.

00:30 Food in their diets.

00:32 So now what we want to check is assuming that we want to be, in this case, consider 1 % of significance level, we want to check what, if you can really say here, then now the proportion in the population, the true proportion, is different than what it was in 2014, which is 0 .45%, 45%.

00:58 So this is what we want to.

01:00 To test in our hypothesis, our claim, which is our alternative hypothesis.

01:06 And our new hypothesis is that the proportion hasn't changed, so it is still 45.

01:16 So the idea here is, first, we need to compute what is the p hat, which is the sample proportion of people they are trying to include, like, organic food in their diet, in the sample that was collected.

01:28 So this is the amount of people that said that they are doing that, divided by the total number of people.

01:35 So 2 -1 -0 -0.

01:39 So this here is 0 -5 -1.

01:44 So now considering this, we need to compute the test statistic.

01:49 So the test statistic here is given by the letter z.

01:56 So this test statistic is p hat.

02:00 Minus the true value of p that we are assuming, which is 45, divided by what we call the standard error of our p hat distribution, which is given by p -0, 1 minus p -0, divided by the sample size.

02:20 So this means that we should plug in here, 0 -5 -1, which is the sample proportion, 045, and then here, here we have, like 045, 1 minus 0 .45, divided by 21000.

02:40 So this here will give us 5 .5 to 68 as our test statistic.

02:50 Now, the two approaches that we can use here are this critical value, so the z critical, and the other one is the p value.

03:04 So the critical value here basically what means is that considering our test statistic, we need to compare this value to the critical values that we have for this test.

03:16 So because this test is two -sided or two -tail, why? because we have the different sign here.

03:25 So this means that because we have the different sign, this means that this test is two -sided.

03:30 Or two tail.

03:33 So this means that we have two critical values.

03:36 So the critical values here, which i'm going to write as zc, they are the same in terms of value, but like the sign is different.

03:46 Why they are the same? because we are assuming that p hat, by definition in this case, we are considering that p hat has normal distribution, what is approximately normal, normally distributed...

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