WEBVTT 00:02.750 --> 00:06.950 In this session, we will discuss about confidence in those run for the. 00:08.180 --> 00:16.220 So let us discuss about an example, so a scientist is interested in monitoring chemical contaminants 00:16.220 --> 00:16.820 in food. 00:17.860 --> 00:22.710 And thereby the accumulation of contaminants in human diet. 00:23.770 --> 00:29.250 Selected a random sample of in equal to four female adults. 00:30.250 --> 00:38.890 It was found that the average daily intake of dairy products was seven fifty six grams with a standard 00:38.890 --> 00:40.810 deviation of thirty five grams. 00:41.470 --> 00:44.470 So here we have the sample size. 00:45.280 --> 00:48.310 We have the mean value. 00:49.580 --> 00:54.640 And we have the standard deviation value, which is related to the sample itself. 00:56.390 --> 00:58.110 Now we need to find out. 00:58.130 --> 01:01.130 Ninety five percent confidence interval for this. 01:02.470 --> 01:09.220 So how do we find out 95 percent confidence interval, so we have to find out 95 percent confidence 01:09.220 --> 01:09.670 interval. 01:09.700 --> 01:18.310 So it will be equal to X value, the mean value plus and minus the Z value. 01:19.580 --> 01:21.230 Into the. 01:22.160 --> 01:24.680 Standard deviation divided by road and. 01:26.290 --> 01:28.180 Which is the standard deviation of the. 01:29.830 --> 01:31.220 Actual population. 01:32.230 --> 01:34.250 So what do we get here? 01:34.270 --> 01:36.890 We are finding out the value. 01:36.940 --> 01:39.130 So what is the mean value? 01:39.160 --> 01:40.300 Seven fifty six. 01:41.510 --> 01:50.030 And we have, as we have ruled, fafi as the square root of N. 01:51.000 --> 01:57.150 Which is the sample size and one point nine six is the Z value. 01:59.720 --> 02:01.850 So how do we find out the Z value? 02:01.880 --> 02:03.590 These are standard Z values. 02:18.310 --> 02:20.770 So here we have the standard Z value. 02:22.120 --> 02:27.730 So we want to have the value as five person. 02:29.370 --> 02:31.320 The conference in Deauville has to be. 02:32.550 --> 02:36.300 Ninety five percent of the alpha value will be zero point zero five. 02:38.600 --> 02:47.720 And for zero point zero five, the corresponding Z score is one point nine six two two point favorite. 02:48.260 --> 02:50.400 So we can say that only one point nine six. 02:51.140 --> 02:53.520 So we consider one point nine six. 02:53.840 --> 03:00.320 So any value which is falling beyond one point nine six is not in our confidence. 03:00.620 --> 03:05.140 And any value beyond minus one point nine six is again in not confidence. 03:05.420 --> 03:08.570 So we want to find out only this one area. 03:08.810 --> 03:12.760 So the value here is one point nine six and one point ninety. 03:12.820 --> 03:18.260 So we are multiplying one point nine six with the estimated value then, which is the standard error 03:18.860 --> 03:19.320 value. 03:20.060 --> 03:21.140 So what do we get? 03:23.440 --> 03:24.130 So we get. 03:25.220 --> 03:30.950 Seven for physics, plus minus nine point seven zero, which is the confidence in for. 03:31.670 --> 03:36.920 This is the confidence interval from you and the confidence level is ninety five percent confident. 03:42.080 --> 03:48.290 Now, being ninety five percent confident means that if you were to construct a hundred ninety five 03:48.290 --> 03:55.090 percent confidence intervals from a hundred different random samples out of the hundreds in the woods, 03:55.340 --> 04:01.490 you expect 95 to capture the true me and five not recapture them. 04:02.360 --> 04:07.700 In conclusion, you cannot be sure that a specific confidence interval captures the bromine. 04:08.900 --> 04:16.850 So that is why we find out the confidence and now the margin of error for this estimation is this value 04:17.630 --> 04:20.000 to Sigma Bond Rubini. 04:20.920 --> 04:27.640 It determines the precision in the estimation of you for a fixed confidence level, increasing the sample 04:27.640 --> 04:30.560 size improves the decision of estimation. 04:30.820 --> 04:34.450 So in case we want to have the. 04:35.670 --> 04:37.390 Confidence in the world as fixed. 04:37.740 --> 04:45.630 That is the value we want to give the Z value fixed, then if we want to decrease the value of this 04:45.630 --> 04:46.070 error. 04:47.460 --> 04:52.980 So in that case, we will have to increase the value of those campuses. 04:53.990 --> 04:57.630 Because it is inversely proportional to the error value. 04:57.830 --> 05:05.290 So if the error value will be less, then this value which we are adding and subtracted from the mean 05:05.300 --> 05:06.700 value will be lesser. 05:06.740 --> 05:08.890 And the answer would be more precise. 05:12.820 --> 05:20.470 Now, a random sample of two hundred nurses is taking on each nurse asked his own her annual income 05:20.830 --> 05:22.150 in dollars. 05:23.230 --> 05:27.130 Now, these two hundred nurses have an average income of thirty five thousand. 05:28.300 --> 05:35.270 With a standard deviation of five thousand, so then the 90 percent confidence will then be gathered. 05:35.290 --> 05:42.310 This will be thirty four thousand thirty five thousand, which will be eleven and seventy dollars. 05:43.150 --> 05:46.270 Similarly, 95 percent confidence interval will be. 05:47.170 --> 05:51.640 Thirty nine dollars and ninety nine percent confidence interval will be. 05:57.270 --> 06:05.100 One eight three you so you can see when we increase the confidence interval, when we increase the percentage 06:05.100 --> 06:09.420 of confidence, the size of the confidence interval also increases. 06:15.010 --> 06:18.640 Now, let us look at different elements affecting the confidence in. 06:19.660 --> 06:23.950 So when we have the standard error. 06:25.010 --> 06:27.380 So when the standard error decreases. 06:30.660 --> 06:37.190 With the increase in the sample size, so the optimal sample size rather than maximum sample size, 06:37.190 --> 06:44.310 so when the standard error decreases, the confidence interval again would change, then we have standard 06:44.310 --> 06:44.970 deviation. 06:46.570 --> 06:53.080 The less variability in the sample, the more precise the estimation in the population and therefore 06:53.080 --> 07:01.590 the narrower the range of samples will be less variable, then the range will be more narrower. 07:02.980 --> 07:10.960 And then there is a degree, the more confident we want to be, the higher the confidence interval has 07:10.960 --> 07:11.190 to be. 07:14.530 --> 07:17.230 Next, we will discuss about how this is testing.