5. In a sample of 1000 people in Maharashtra, 540 are rice...

Name: 5. In a sample of 1000 people in Maharashtra, 540 are rice eaters and rest are wheat eaters. Can we assume that both rice and wheat eaters are equally popular in this state at a) 5% level of significance b) 1% level of significance?
Uploaded: 2025-01-07T12:45:55-08:00
Duration: 5 min 32 s
Channel: Joanna Quigley
Description: 5. In a sample of 1000 people in Maharashtra, 540 are rice eaters and rest are wheat eaters. Can we assume that both rice and wheat eaters are equally popular in this state at a) 5% level of significance b) 1% level of significance?

5. In a sample of 1000 people in Maharashtra, 540 are rice eaters and rest are wheat eaters. Can we assume that both rice and wheat eaters are equally popular in this state at a) 5% level of significance b) 1% level of significance?

Transcript

00:01 We have a sample of 1 ,000 people.

00:03 540 eat rice, the rest eat wheat.

00:06 Can we assume that both are equally popular? so what kind of test should we be doing here? well, we have one sample, and we're looking at two proportions within it.

00:18 The proportion that eat rice, the proportion to eat wheat.

00:21 So you might be thinking, okay, i'm comparing proportion of rice to proportion of wheat.

00:25 Maybe i need a two proportion test.

00:28 But that wouldn't be the case because these are directly.

00:31 Dependent on each other.

00:33 You can either be a rice eater or a wheat eater, so the wheat eaters will just be 100 % minus the rice eaters.

00:39 So actually, this is a one proportion test.

00:47 So let me state my hypotheses.

00:51 My null hypothesis would be that they are equally popular.

00:55 There's no difference between them.

00:57 So p, we'll look at rice, proportion of rice eaters would be 0 .5 or 50%.

01:03 And therefore, proportion of rice eaters and proportion of wheat eaters would be equal.

01:07 The alternative is that they are not the same, and the proportion for rice eaters is not 0 .5.

01:13 The null hypothesis always gets some kind of equal sign.

01:16 It represents no change or no difference.

01:20 Our sample is size 1 ,000, and out of these, 540 eat rice, giving us a sample proportion of 0 .54.

01:30 540 out of 1 ,000.

01:34 To perform a hypothesis test, we start by assuming the non -hypothesis is true.

01:39 And we look at the distribution of the possible sample proportions we would see here.

01:45 If i took every sample of size at 1 ,000, took the proportions that eat rice, plotted them all out, i would get something approximately normal, thanks to the central limit theorem.

01:57 So this is the distribution of p hat, approximately normal.

02:01 Its mean is p, its standard deviation is root p1 minus p over n.

02:09 So we think p is 0 .5.

02:12 So 0 .5 would be in the middle here.

02:14 Now where would my p hat fall on this curve? maybe it was here.

02:19 It's not 0 .5 but it's pretty close.

02:23 It is plausible that this sample proportion belongs to this distribution and that p is 0 .5.

02:30 But if my sample proportion is way out here, i would say, if the null hypothesis is true, this is really unlikely to happen.

02:39 Therefore, don't think it's true.

02:41 Then we reject it.

02:43 The level of significance in part a is 5%.

02:47 It tells you how unlikely it has to be before you reject it...