WEBVTT 00:01.640 --> 00:04.860 In this session, we will discuss about confidence in those. 00:05.980 --> 00:13.900 A confidence interval refers to the probability that a population barometer will fall between two sets 00:13.900 --> 00:16.470 of values for a certain proportion of times. 00:18.950 --> 00:25.630 Confidence intervals measure the degree of uncertainty and also in the sampling method. 00:27.220 --> 00:28.960 Now, let us look at this. 00:35.810 --> 00:37.990 Neighbors say they have this particular data. 00:39.660 --> 00:45.540 And we want to debate that there is a particular value see 25. 00:46.680 --> 00:53.070 And we want to find out if the 25 value actually falls in this normal. 00:54.930 --> 01:03.360 So confident Sandoval will be able to provide us a probability that there is a little if for people 01:03.360 --> 01:12.150 are saying or 90 percent or 100 percent chance that 20 will be falling in this good or twenty five will 01:12.150 --> 01:13.310 be falling in this cycle. 01:14.190 --> 01:16.530 So this is what confidence in Bellevue's. 01:17.570 --> 01:23.610 So we will get the probability like this is the probability that this value will fall in the Gulf. 01:23.890 --> 01:27.690 And what is the limit around which it will be present? 01:28.550 --> 01:36.480 So let us say it will give an interval that the value will be present between 20 and 24. 01:37.440 --> 01:43.850 Or let us see the value will be preserved between 18 and 22 from our previous example. 01:44.870 --> 01:52.040 Like the meaning of this particular distribution will be from 18 to 22 now, the confidence associated 01:52.040 --> 01:53.600 will be a different value. 01:53.900 --> 01:56.300 So this is what the confidence interval is. 01:56.300 --> 02:04.100 Confidence interval is basically a value or range which provides a probability barometer that something 02:04.100 --> 02:06.290 will fall between two sets of values. 02:07.980 --> 02:12.680 Now, some properties of this is that it will be symmetric about the meaning of data. 02:14.280 --> 02:18.770 Any convincing interval will be symmetric about the meaning of the data. 02:19.750 --> 02:25.780 Confidence in the will can have differing degrees of confidence, such as 60 percent confidence, 80 02:25.780 --> 02:26.770 percent confidence. 02:26.780 --> 02:28.480 Ninety nine percent confidence. 02:29.020 --> 02:35.650 This forcing the confidence means that out of a hundred samples taken. 02:36.760 --> 02:41.710 60 samples will have this particular mean value. 02:43.840 --> 02:46.720 We have an arrest we are not sure of. 02:47.890 --> 02:57.350 Similarly, 99 percent confidence means that out of a hundred samples, the mean value will be X and 02:57.370 --> 03:00.990 that will be in 99 of the samples out of hundreds. 03:03.250 --> 03:07.560 Now, greater the sample size, smaller the confidence interval. 03:08.380 --> 03:15.700 So when we are taking let's say we have 100 population values, our population has hundred values, 03:16.150 --> 03:20.050 and I'm taking a sample of, say, only 20 values. 03:20.950 --> 03:24.730 So their confidence interval will be larger. 03:25.820 --> 03:33.680 Because I am not sure if I'm taking only 20 values as a sample, then the window of the confidence interval 03:33.680 --> 03:40.960 will be larger because when my sample sizes one, I will not be able to be sure about that. 03:41.240 --> 03:43.190 What will be the range of the meat? 03:43.970 --> 03:46.280 So if I will, I have only 20 values. 03:46.280 --> 03:52.990 I will not be sure that the machine will be exactly 20 or it will be 18 or it will be 16. 03:53.150 --> 03:59.990 I might say that if there are only 20 values which I have got in the sample and the population sizes. 04:00.620 --> 04:01.580 So maybe. 04:02.680 --> 04:13.240 The mean good to be around see 30 to 60, I can say something like that, but when I have around 70 04:13.240 --> 04:23.020 values in my sample and then I have the mean of my sample as 50, then I can see with more confidence 04:23.020 --> 04:27.140 that the value of the machine will be somewhat around 50. 04:27.160 --> 04:32.230 So let us see that it will be around forty five to fifty five. 04:32.440 --> 04:34.480 I can be more precise. 04:34.480 --> 04:41.620 I can be more sure because my population size is somewhat near to the sample size and then the sample 04:41.620 --> 04:45.100 size will be exactly the same as the population size. 04:45.370 --> 04:48.320 Then I will be 100 percent sure what my means. 04:48.910 --> 04:51.610 So the confidence interval will be more moyet. 04:53.180 --> 04:59.240 So this is what the states, the greater the sample size, the smaller the confidence interval that 04:59.240 --> 05:06.110 is more accurate determination of the population mean from the sample mean different sample means will 05:06.110 --> 05:08.450 have some different confidence in votes. 05:08.930 --> 05:16.130 So if they have one sample, it has different of one sample mean and there is another sample which has 05:16.400 --> 05:17.630 another sample mean. 05:17.870 --> 05:21.410 So the confidence interval will also be different for both of these. 05:26.940 --> 05:27.480 Now. 05:30.530 --> 05:38.180 Here, one minus Alpha gives the probability that the true value falls into the calculated interval. 05:39.450 --> 05:43.250 OK, so we can also give a confidence level in person. 05:44.160 --> 05:46.410 So what will be the confidence level? 05:46.420 --> 05:52.800 Let's say we have a confidence level of 90 percent, 95 percent or 99 percent legacy. 05:52.800 --> 05:58.410 I work in an organization and they want me to provide me that. 05:58.410 --> 06:01.200 There is I want I have to give them that. 06:01.200 --> 06:07.140 I am 95 percent sure what should be the mean of the something I need to provide this particular data 06:07.290 --> 06:13.910 that what should be the mean of a particular population based on the sample which I have and I want 06:13.920 --> 06:19.260 I have to be 95 percent sure, then what I will do is I will be considering the. 06:20.640 --> 06:24.270 Alpha value as ninety five percent. 06:25.580 --> 06:30.150 So what will I have, one minus Alpha as five percent. 06:30.980 --> 06:35.500 So here's my alpha value will be five percent, which is zero point zero five. 06:36.110 --> 06:43.220 So I will be calculating my alpha value, my Z barometer, the critical region, whatever values I will 06:43.220 --> 06:48.830 be calculating for this confidence interval on the basis of alpha value, considering at zero point 06:48.830 --> 06:49.360 zero five. 06:50.500 --> 06:54.110 This will be my criteria now how we use this criteria. 06:54.130 --> 06:59.800 We will learn about it, but for now, just try to understand that when I want to have a confidence 06:59.800 --> 07:06.490 interval, when I want to determine something, when I want to determine a population barometer, I 07:06.490 --> 07:12.530 have to provide my insight on some confidence level. 07:13.150 --> 07:15.890 I have to provide the confidence level. 07:16.540 --> 07:17.800 So let us see. 07:17.800 --> 07:21.840 My organization wants me to be 95 percent confident. 07:22.180 --> 07:26.670 So in that case, my confidence interval would have to be 95 percent. 07:27.100 --> 07:35.540 So my one minus alpha value one will be the probability eight out of a hundred percent. 07:35.560 --> 07:37.580 I want to be 95 percent sure. 07:37.990 --> 07:42.670 So the confidence interval, the range of the interval has to be five percent. 07:44.560 --> 07:45.940 And what is five percent? 07:46.240 --> 07:48.880 Five percent is equal to zero point zero five. 07:50.050 --> 07:56.620 So then I'm looking at only one direction, it will be zero point zero one zero point zero two five 07:56.620 --> 07:58.890 days, we will look at it for now. 07:58.900 --> 08:00.610 You can ignore this entire thing. 08:01.210 --> 08:05.170 Just remember that my alpha level will be zero point zero for. 08:07.370 --> 08:10.160 So we can give the confidence level in person. 08:10.370 --> 08:15.530 So this is a confidence interval, the most in the confidence interval at informal point, that's going 08:15.530 --> 08:16.960 to be the margin of error. 08:17.330 --> 08:19.390 So we will have some value. 08:19.400 --> 08:22.340 We will have some mean value, which we will calculate. 08:23.000 --> 08:32.870 And based on this value, we will give up value in the will value a margin value that I am sure that 08:32.930 --> 08:34.790 the mean for me is 50. 08:35.630 --> 08:44.640 So from this mean 50, the confidence in those states that there can be an error of five in this. 08:44.840 --> 08:52.310 So when I say five, so it will be my mean value, minus five, I mean value plus five, anything would 08:52.310 --> 08:52.830 be of value. 08:53.090 --> 08:57.290 So the value could be either 45 or 50. 08:57.770 --> 09:00.080 It could be between forty five and fifty five. 09:00.080 --> 09:05.190 For me the value is fifty, but there is a margin of error of five. 09:05.690 --> 09:07.970 So the value can range from 45 to 50. 09:08.540 --> 09:11.600 This is what how a confidence interval would be stupid. 09:13.100 --> 09:18.680 And this I will be determining on the basis of the confidence interval how we going to do this while 09:18.980 --> 09:21.590 we're doing this, we will look at it in something. 09:23.900 --> 09:24.440 Now. 09:27.270 --> 09:29.790 We will be having certain range of values. 09:30.740 --> 09:36.230 So the values will be now this interval, the confidence interval, which we will be having. 09:36.260 --> 09:44.390 So my task is to find out the mean value value I have to find out mean of my population and the mean 09:44.390 --> 09:47.210 of the population will be the central value of my flock. 09:49.180 --> 09:56.710 Now, I have one son, Bill, and I have a mean value now, the exact value of the population mean could 09:56.710 --> 10:00.360 be a little bit higher also and a little bit towards the right side. 10:00.370 --> 10:05.280 Also, either the value will be towards left, either the value will be towards right. 10:06.100 --> 10:11.960 So it will be either plus two, minus two or it will be plus three, minus three and accordingly. 10:12.620 --> 10:15.160 OK, so it will be symmetric in nature. 10:16.420 --> 10:20.960 Now, the confidence level will be one minus Alpha, which we have already discussed. 10:21.400 --> 10:23.920 Now the value of the range will be. 10:25.270 --> 10:34.240 It'll be this value will be it, and this value will be we are seeing the value will be between 45 and 10:34.240 --> 10:38.050 55, so forty five will be it and 55. 10:38.050 --> 10:41.260 Will we be with the meanest 50? 10:42.290 --> 10:45.440 Now, how will we find out the probability? 10:47.190 --> 10:53.250 The probability of success, what we are seeing here is now we are seeing that this is the change we 10:53.250 --> 10:59.250 provide, the mean value we provide, the minimum value and the maximum value we provide the margin 10:59.250 --> 11:01.530 value also that this is the margin value. 11:01.530 --> 11:06.210 It will be either a less minus five or less like this. 11:06.220 --> 11:08.520 It will be 50 minus five. 11:08.670 --> 11:12.660 That is 40 or 50 plus five, that is. 11:13.770 --> 11:14.420 Fifty eight. 11:15.610 --> 11:21.190 So when I have a percentage in it, I have an interval of. 11:23.220 --> 11:24.270 Five percent. 11:25.380 --> 11:33.110 When I have an interval of five percent, when I have an interval of ninety five percent pure. 11:34.100 --> 11:35.820 This is one minus Alpha. 11:36.470 --> 11:38.360 What was my confidence in the. 11:40.400 --> 11:46.460 My confidence interval was like us in 95, it's not dead in this gives Nickerson, in this case, we 11:46.460 --> 11:48.510 have confidence in the will of 90 percent. 11:49.350 --> 11:55.820 OK, and now in that scenario, we are considering the confidence in the will of nine people. 11:56.780 --> 11:58.130 So what will this be? 11:58.340 --> 12:01.180 This will be one this will be 90 percent. 12:01.610 --> 12:08.470 So the 90 percent of data will be 90 percent of the values will be present under this plot. 12:09.980 --> 12:12.800 Ninety percent of the values will be present, this blog. 12:13.880 --> 12:15.920 So the value which we are looking at. 12:17.940 --> 12:26.790 Will be under this 90 percent I have I am going to be 90 percent sure that the value is lying between 12:26.790 --> 12:27.120 this. 12:28.340 --> 12:36.110 Ninety percent of the area of the plot I'm covering and I'm seeing that the confidence is 90 percent. 12:37.170 --> 12:38.960 So what am I losing at? 12:39.860 --> 12:41.870 I am losing Aftenposten. 12:43.140 --> 12:45.140 I am not confident by that. 12:46.170 --> 12:47.650 What am I not confident of it? 12:48.060 --> 12:50.970 I am not confident with the enforcement of that. 12:51.780 --> 12:54.000 So I am not confident that enforcing. 12:56.550 --> 13:04.620 So this is 90 percent and this is a joke, this is a symmetric distribution, so the 10 percent will 13:04.620 --> 13:06.670 be divided between this part and this part. 13:07.290 --> 13:11.610 So this idea will again have five percent and this CGI will also have five percent. 13:15.070 --> 13:18.070 So that is why we have this. 13:19.110 --> 13:20.040 AlphaBeta. 13:21.340 --> 13:22.270 Zero point zero. 13:25.630 --> 13:27.310 So this is all we can find out. 13:27.340 --> 13:29.150 The confidence interval. 13:29.170 --> 13:30.400 So how will we find out? 13:30.410 --> 13:32.110 Confidence interval now. 13:33.350 --> 13:40.040 Think in themselves, they think in terms of how we would calculate things, if we have certain value 13:40.040 --> 13:47.240 of the sampling distribution, we had some distribution, we had a sample here and in the sample we 13:47.240 --> 13:48.930 had some distribution of data. 13:48.950 --> 13:55.060 We said the values are ranging from one, two hundred and from these values ranging from one 200. 13:55.070 --> 13:57.290 We have 50 here, which is the mean value. 13:58.660 --> 14:05.650 And this is the distribution of the data and from this distribution of data, we want to find out what 14:05.650 --> 14:13.300 should be the population me now my population has a lot more values presently, say a thousand or two 14:13.300 --> 14:14.950 thousand or five thousand views. 14:15.130 --> 14:20.850 So I'm not sure if this 50 is actually the mean of my population. 14:21.310 --> 14:29.950 So that is why to my organization or to my manager I want to provide the means should be something between 14:29.950 --> 14:30.900 some range. 14:30.910 --> 14:33.460 The is between the range and the. 14:33.640 --> 14:35.890 But I am not sure what envy's. 14:36.460 --> 14:37.900 So my manager asked me that. 14:37.950 --> 14:40.650 What is the percentage, what is how much confidence. 14:40.780 --> 14:41.000 What. 14:41.260 --> 14:43.900 So give me some confidence level that you are ninety. 14:44.080 --> 14:50.440 Something like you, you will be 90 percent sure that between which the value should be changing so 14:50.440 --> 14:57.490 you give them the value should be ranging between this and this, which is 90 percent of my data. 14:58.520 --> 15:03.650 Which is 90 percent of my data, so it will be changing between this area. 15:04.040 --> 15:11.570 Now, this area is owned by me, so that is why I will be left with five percent here and five percent 15:11.570 --> 15:11.810 here. 15:12.620 --> 15:15.490 So this much complete area will be 90 percent. 15:15.500 --> 15:19.640 So if I give this range, so 90 percent of my data will be covered inside this. 15:19.650 --> 15:23.450 So I can say I'm 90 percent sure that the machine will be lying within this. 15:25.270 --> 15:32.200 So now our focus is to find out what does this value and what does this value and how do we find that 15:32.200 --> 15:32.390 out? 15:32.410 --> 15:36.460 We we find that out based on the z value which we have used. 15:37.090 --> 15:39.180 And how do we find the Z value? 15:39.190 --> 15:42.880 The Z value is followed based on this X. 15:43.920 --> 15:47.640 X minus mu divided by. 15:48.570 --> 15:49.170 Sigma. 15:51.030 --> 15:58.020 So based on that, I can find out the value and now we don't have the X value here, we don't have the 15:58.020 --> 16:01.840 X value, but we know the Z school what what the Z score should be. 16:02.220 --> 16:04.200 So we will find out the Z score. 16:04.410 --> 16:09.510 And based on the score, we can find out what the value should be and hence we will be able to find 16:09.660 --> 16:12.680 the confidence and now we will see how they do that. 16:12.840 --> 16:19.230 But they know this is just theoretically how we will be finding out the confidence in the will and the 16:19.230 --> 16:20.240 confidence level. 16:22.290 --> 16:25.440 This is one example which we will be discussing about this. 16:26.760 --> 16:27.690 In the next session.