WEBVTT 00:02.210 --> 00:07.970 In this session, we will discuss about the and different views of the best. 00:09.020 --> 00:16.360 So they have been using the test so that we could compare the population on a sample. 00:17.770 --> 00:22.450 But in a few cases, they cannot use best. 00:23.790 --> 00:25.320 So that does when. 00:27.360 --> 00:35.460 Using Z is not always possible, as we would not have the population barometers always handy. 00:36.390 --> 00:44.340 So in case we don't have any population barometers, so in those scenarios, we will not be able to 00:44.340 --> 00:51.300 use the Zionist, hence the use of the abortion, which is students the disc. 00:53.020 --> 00:58.450 We can use the deepest if something has size below 30. 00:59.850 --> 01:03.780 And it has a population standard deviations. 01:05.010 --> 01:05.850 For example. 01:07.920 --> 01:18.120 We have an assumption that is the data is independent, it is collected randomly and the data is approximately 01:18.510 --> 01:20.070 normally distributed. 01:21.610 --> 01:29.520 I'm the interpretation of the issue is when when we find out that the value you finding out that the 01:29.530 --> 01:38.380 value is just similar as the Z value, the formulas are almost similar and how we interpret the data 01:38.680 --> 01:39.820 is slightly different. 01:40.270 --> 01:50.200 So if the calculated the value in the is less than the value of the table, then if the value is less 01:50.200 --> 01:57.580 than zero point zero five or zero point zero one, the level which is present at zero point zero five 01:57.940 --> 02:01.610 0.01, then the null hypothesis is accepted. 02:02.770 --> 02:06.580 It is just similar to the Z value. 02:06.730 --> 02:15.310 So in the Z value, we had to provide the alpha level in the Z table while we were calculating the value 02:15.580 --> 02:24.310 we originally had to provide all alpha level and based on the alpha level behind the Z value, which 02:24.310 --> 02:25.750 was one point nine six. 02:26.690 --> 02:33.380 In case of zero point zero five, but then piece of detail, we do not have any such alpha. 02:34.100 --> 02:38.110 We have alpha level person that is in the basement. 02:38.330 --> 02:46.850 So what we do is we find out the value which we want to compare and we check if the value is present 02:46.850 --> 02:48.080 in the basement. 02:48.380 --> 02:55.580 I'm in the they will become very from the levels of zero point zero point zero one. 02:56.850 --> 03:05.310 If the value is less, then the value is present at zero point zero five or zero point zero one, then 03:05.550 --> 03:12.630 the null hypothesis is accepted and increase the likelihood that the value is greater than that which 03:12.630 --> 03:17.180 is present in the people at zero point zero five or 0.01. 03:17.400 --> 03:19.020 Then the null hypothesis. 03:19.200 --> 03:20.280 David A.. 03:22.430 --> 03:25.980 So let's go for that and see how this actually works. 03:26.210 --> 03:34.760 So there are three types of B this one is the one somebody, just the one somebody. 03:34.760 --> 03:42.050 This is used when we have a single group of data and we want to take this group against against one 03:42.050 --> 03:44.980 when we have some some single group of data. 03:44.990 --> 03:49.730 And we want to check this against an already known value from the population. 03:51.580 --> 03:58.540 And that is the independence of graffitists, this independence, empathy, this is where we have two 03:58.540 --> 04:07.330 independent groups that we have some data of flu samples and these samples belong to different categories, 04:07.330 --> 04:14.200 except one category would be under the category could be Fehmi or one category would be students from 04:14.200 --> 04:15.260 one university. 04:15.320 --> 04:21.790 I'm under the guise of clinical research from the second university or one category could be the same 04:22.060 --> 04:27.160 people from one city and under the category could be people from another city. 04:27.370 --> 04:31.890 So the sample which is taken belongs to two different groups of people. 04:33.330 --> 04:40.020 And if they are, this is when they are checking on the same group, but they are checking out different 04:40.020 --> 04:43.530 conditions, we are taking a different time. 04:43.530 --> 04:46.650 We will see they are checking out one year of difference. 04:46.860 --> 04:48.720 So this is going to hurt somebody. 04:51.200 --> 04:58.340 So now to see one question which would actually explain this, how this is working. 05:02.790 --> 05:04.350 So here we have. 05:05.360 --> 05:07.380 Again, the same Juden question. 05:07.850 --> 05:13.560 So what do we have here is we have a study of the status of critically ill children. 05:13.850 --> 05:20.180 So here again, we have 16 children with the permanency out of these children. 05:20.720 --> 05:28.280 They have 12 of one point, the number of missing beat and the standard deviation is one point nine. 05:29.270 --> 05:35.330 And the actual win is one point four, which is already pretty clear. 05:35.600 --> 05:42.080 Now you can see the definition of when somebody's desk, which is the meaning of a single group against 05:42.080 --> 05:42.410 a wall. 05:43.580 --> 05:47.870 So this is one group which we have where we have 16 children. 05:50.750 --> 05:57.020 It is found that the number of missing will be this one point and the standard deviation is one point 05:57.020 --> 05:59.270 nine and the actual nine. 06:00.570 --> 06:10.920 This already one mean single group against me, so this is the only one point four, so this is being 06:10.930 --> 06:14.800 the only want to find out if they'll mean the same or different. 06:15.090 --> 06:16.350 So how do we do this? 06:17.640 --> 06:25.590 So the hypothesis is that the mean is actually equal to one point for. 06:27.030 --> 06:31.530 And another hypothesis is that the line is not equal to one point for. 06:32.710 --> 06:41.970 And that is the mean of the student are having this critical illness is one point for and here the is 06:42.360 --> 06:43.580 not one point for. 06:44.190 --> 06:47.820 So the data is and is equal to 60. 06:48.930 --> 06:52.950 So that is NWC in the Sanford. 06:54.110 --> 07:00.960 Now, the test statistic is so people estimate of population barometer deriving from this data. 07:01.160 --> 07:05.930 So we have the median value, the average mean value at one point to. 07:08.340 --> 07:14.130 And we are performing the one simple thing that's doing this so that the value will be. 07:15.250 --> 07:19.390 Exper minus meal divided by. 07:20.800 --> 07:22.620 Those standard errors. 07:23.590 --> 07:32.800 In the Z formula, in the formula for Z value, the formula used to be exper minus new, divided by 07:32.980 --> 07:36.750 the standard deviation of the population by here. 07:37.090 --> 07:45.460 This is divided by the standard deviation for the sample, which is the standard error divided by the 07:45.520 --> 07:50.120 number of sample, which is how we calculate the standard deviation. 07:50.590 --> 07:55.900 So we are finding out one point two minus one point four divided by one point nine. 07:57.010 --> 08:03.870 From this outfit, and this is the size of the sample in Swaroop, so we find out the value minus point 08:04.330 --> 08:05.170 for the one. 08:06.140 --> 08:08.030 Now, this is the P-value. 08:09.030 --> 08:12.210 Now we need to check the P in the. 08:14.370 --> 08:19.110 Now, how does the detainee rule in that be able to have these? 08:22.530 --> 08:30.070 So this is one column which is having so numeric values and this has given us a degree of freedom. 08:31.320 --> 08:40.770 What is degree of freedom we will look at just in a few minutes and this rule that Alpro contains the 08:40.770 --> 08:41.700 probability. 08:42.610 --> 08:49.570 That is what is the probability for having the confidence I'm here, we have the. 08:50.650 --> 08:57.670 One day this time, to be honest, that is if they are taking in one direction or we are checking in 08:57.690 --> 08:58.860 both directions. 08:59.560 --> 09:01.720 So when we're talking about. 09:03.880 --> 09:06.580 Meal is not equal to one point four. 09:06.910 --> 09:15.120 This means that you can be less than one point for total and you can be greater than one point for all. 09:15.520 --> 09:16.840 It can have any value. 09:17.080 --> 09:18.160 There is no restriction. 09:18.160 --> 09:22.840 That meal has to be greater than one point for only or has to be less than one point for only. 09:23.140 --> 09:26.510 Here, meal can be any value in any direction. 09:27.280 --> 09:30.270 So then you can have any protection. 09:30.520 --> 09:34.240 This means then it can be a part of any of the two bills. 09:35.400 --> 09:36.860 If we look at this blog. 09:39.790 --> 09:48.370 And so if nobody value is the central idea, then be accepted null hypothesis, if it belongs to any 09:48.370 --> 09:52.600 of these stupid idea, then it is a part of the rejection region. 09:52.630 --> 09:54.980 So this is the data and this is being rejected. 09:55.270 --> 10:00.020 So now the P value will be divided into two parts. 10:00.670 --> 10:04.870 So initially, if we were taking in only one direction, let us see. 10:04.870 --> 10:09.080 The condition would have been mbewe is greater than 40. 10:09.910 --> 10:17.110 If the view is greater than for being this is an addiction criteria, then we will have only one because 10:17.110 --> 10:24.220 we are not checking for the Lordi when we are seeing new is greater than 14, then we are not checking 10:24.220 --> 10:28.560 in this direction because here we are sure that it is more or less than 40. 10:28.810 --> 10:31.530 We are just checking new is greater than for being here. 10:32.460 --> 10:34.060 So it didn't look like an addiction. 10:34.070 --> 10:36.760 Gladia will be only one beat back. 10:36.910 --> 10:45.700 The Godding hypothesis is that new is not equal to forty or one point four in the scenario. 10:45.820 --> 10:53.410 So new is not equal to one point, which means that it has to be significantly far away from one point 10:53.410 --> 10:55.200 for in any of the directions. 10:55.450 --> 10:58.150 So now the problem is all these. 10:59.110 --> 11:04.990 So then the problem would have been in one field, if the problem would have been in one single thing, 11:05.230 --> 11:09.520 then we will have zero point five percent data here. 11:10.240 --> 11:13.720 The critical region would have been zero point five in this area. 11:15.190 --> 11:22.180 But now, because we are talking about both directions, so the zero point five will be split in two 11:22.520 --> 11:23.820 border regions. 11:23.950 --> 11:29.140 So this will have zero point to fight and this will have zero point zero two five. 11:29.650 --> 11:33.130 So the zero point five will be divided into two. 11:33.430 --> 11:40.150 And we will check for zero point two five level here and zero point zero five level here, zero point 11:40.150 --> 11:43.410 zero zero five level here and zero point zero five here. 11:48.860 --> 11:50.780 So this is the value. 11:53.140 --> 11:55.390 So now we will check for. 11:56.920 --> 12:05.290 Zero point five, so zero point five, in case of one day, if there were boobies, then we would have 12:05.290 --> 12:07.790 checked for zero point one zero. 12:08.140 --> 12:08.920 Similarly. 12:10.530 --> 12:18.480 Here we have zero point zero to five in case of one day, and he will we have zero point zero five. 12:21.890 --> 12:27.440 So in this particular case, we will be finding out the values accordingly. 12:27.680 --> 12:29.150 So let us have a look at this. 12:30.260 --> 12:38.780 So here the number of values that we have, the number of values in the sample that we have is 16. 12:40.670 --> 12:46.820 Now, let us survive, this is prominent, so we have to find out the degree of freedom. 12:48.060 --> 12:51.310 This particular column here refers to the degree of freedom. 12:51.570 --> 12:53.670 So how do we find the degree of freedom? 12:54.850 --> 13:03.490 The degree of freedom is the number of values that we can select independently with one restriction. 13:04.470 --> 13:12.330 So when we are taking out the sample, because the mean has to be of value, which is in between, so 13:12.330 --> 13:16.820 we even be selecting different values independently. 13:17.190 --> 13:20.670 So let's say we have total 50 values, which you want to pick. 13:20.670 --> 13:25.260 OK, then we can restrict, say, 16 values. 13:25.530 --> 13:30.390 Then if we restrict this one value here, if then what? 13:30.510 --> 13:32.310 Then how many values can we have? 13:32.310 --> 13:36.630 We can select one to three values independently. 13:36.900 --> 13:45.990 So out of this one, two, three and four values, we can select three values without any hesitation. 13:45.990 --> 13:48.750 We can select any values as these three values. 13:49.590 --> 13:55.100 By selecting this one value, we will have to make sure that the sum will be equal to four. 13:56.370 --> 13:58.250 So this is what degree of freedom is. 13:58.470 --> 14:03.180 So in case we have these 16 values which we are trying to pick out. 14:03.420 --> 14:08.610 So out of these 16 children, we can pick 15 values independently. 14:08.820 --> 14:18.490 But for the one last value, we will have to make sure that the mean comes out to be, which is simple, 14:18.660 --> 14:21.180 which is as a mean of the population. 14:21.660 --> 14:28.740 So here are the different ways how we can find out different degrees of freedom when we are performing 14:28.740 --> 14:34.500 one somebody's test or bayati this, then the degree of freedom will be in minus one. 14:36.160 --> 14:42.730 When we are working on independently deepest, then the degree of freedom will be in minus two. 14:44.000 --> 14:49.880 When we are walking one guy square, then the degree of freedom will be number of rulers, minus one 14:50.120 --> 14:52.160 in the number of columns, minus one. 14:53.270 --> 14:59.990 When we are working with ANOVA, the degree of freedom between the groups will be number of levels or 14:59.990 --> 15:07.430 groups minus one, and the degree of freedom within the group will be number of subject, minus the 15:07.430 --> 15:10.340 number of levels, what these three are. 15:10.490 --> 15:11.980 We will discuss in something. 15:12.260 --> 15:15.110 But for now, you can remember only these two. 15:15.110 --> 15:18.180 That is number four, that the vest itself. 15:18.440 --> 15:24.860 So in one sample do this and 30 this we will use and minus one, I'm for independent because we will 15:24.860 --> 15:25.920 use in minus two. 15:26.150 --> 15:28.870 So here we have one completist. 15:30.310 --> 15:38.500 So in one somebody this we have an equal to 60, so the degree of freedom will be 50 and the value of 15:38.500 --> 15:42.840 the which we have found is minus zero point four to one. 15:43.270 --> 15:46.090 So we will check for zero point for the one. 15:48.470 --> 15:54.950 So the value zero point four to one lies between these two values, which is somewhat higher. 15:56.520 --> 16:03.960 And it is victorious then this particular value at zero point zero five. 16:05.220 --> 16:06.780 Or zero point zero one. 16:09.130 --> 16:13.490 So here you can see that this value is way less than this value. 16:13.930 --> 16:18.010 So it is anyhow a part of the distribution itself. 16:18.730 --> 16:19.720 This means. 16:21.030 --> 16:21.630 That. 16:22.670 --> 16:31.550 This is just by chance that the methane is coming out to be one point to like the actual minus, one 16:31.550 --> 16:32.570 point for only. 16:33.500 --> 16:38.780 So we can easily accept this hypothesis. 16:39.790 --> 16:41.370 So let us go further. 16:42.690 --> 16:50.160 So you can see that this is these are this is the value, this is minus zero point for the one and this 16:50.160 --> 16:51.790 is minus zero point for the one. 16:52.440 --> 16:55.110 This is where minus zero point six nine one would be. 16:56.640 --> 16:57.870 Zero point six nine one. 16:59.820 --> 17:07.020 This is minus zero point six nine one, so it is way below the actual values which we have for critical 17:07.020 --> 17:07.470 region. 17:09.330 --> 17:13.980 The values are way below the values which are expected for the critical region. 17:14.220 --> 17:21.570 So this is about the zero or one point two is actually a part of the same distribution, which is of 17:21.570 --> 17:23.710 one point one one point for me. 17:24.000 --> 17:26.610 So the hypothesis can be rejected. 17:28.310 --> 17:35.810 So here are a few links for the calculator's, which we have used so we can use this table or this table, 17:35.810 --> 17:42.260 and in case you want to calculate it mathematically and using the calculator without looking at the 17:42.260 --> 17:45.820 people, then you can access the calculator. 17:45.830 --> 17:47.550 I did find Lip-Sync. 17:51.070 --> 17:59.380 Next, we will be looking at the independent sample test, so for the independent sample test, the 17:59.380 --> 18:07.990 assumptions is that one assumption of independence, which means that we need two independent variables, 18:08.260 --> 18:12.830 which is that there should be two different categories which should be represented. 18:13.090 --> 18:20.560 That is something like male or female or another kind of categories could be people from two different 18:20.560 --> 18:24.440 cities or people from two different countries being compared together. 18:24.610 --> 18:29.520 So these are independent samples which are completely exclusive from each other. 18:31.120 --> 18:37.390 So another assumption is assumption of normality, which is that the dependent variable should be approximately 18:37.390 --> 18:43.890 normally distributed dependent, but it should also be measured on a continuous scale. 18:44.710 --> 18:51.550 For example, the test score will be the dependent variable, which is being calculated, and it is 18:51.550 --> 18:54.970 completely independent in nature and it is continuous value. 18:56.480 --> 19:04.400 Now we have another example, so we might face two different groups of customer service associates on 19:04.400 --> 19:10.710 a business related test or testing students from two different universities on their English skills. 19:10.850 --> 19:14.020 So these are different examples of independence for this. 19:16.170 --> 19:18.750 So let us try to solve a problem. 19:20.350 --> 19:22.430 So here we have two datasets. 19:22.840 --> 19:25.480 One is set and that is set to be. 19:26.440 --> 19:31.960 So values for these sects are given to be one, two, two, three, three, four, four, five, five, 19:31.960 --> 19:32.290 six. 19:32.530 --> 19:34.750 And this sect is given to with these values. 19:35.350 --> 19:43.300 Now, we want to find out if these belong to different populations or they belong to the same population 19:43.300 --> 19:48.610 that is in the mean of these two are significantly different or significantly. 19:49.210 --> 19:50.270 So how would we do that? 19:50.290 --> 19:52.430 How would we perform the independent beedis? 19:52.840 --> 19:57.130 So we will do the best by somebody, the values in the groups. 19:57.430 --> 20:02.770 So I have added the values in the first group and the values in the second group, the sum of first 20:02.770 --> 20:07.300 one coming out to be thirty five and the sum of the second one coming out to be 50. 20:09.070 --> 20:18.250 Then we will square the sums from the first step, so the Four-Square is one to do five and second one 20:18.250 --> 20:19.390 is twenty five under. 20:22.130 --> 20:29.960 Now, here we are calculating the mean for the two groups, so the mean will be some of these values 20:29.960 --> 20:34.820 divided by then, so 35 divided by then and four divided by 10. 20:35.060 --> 20:38.030 So we will get them to the three point five and five. 20:39.530 --> 20:43.110 Now we will square the individual scores and then add them up. 20:43.910 --> 20:47.030 So this will be one forty five and ninety eight. 20:49.850 --> 20:54.140 Now, we will insert the numbers in this particular formula. 20:57.980 --> 21:04.340 So when we apply this formula, we have this summation of a square summation of the square in which 21:04.340 --> 21:10.600 we have already calculated these are the means which we have already calculated, the summation of a 21:10.610 --> 21:18.680 square and the sum of squares of data has already been calculated and the number of items has already 21:18.680 --> 21:19.250 been given. 21:19.550 --> 21:23.330 So we will insert all the values in this particular formula, which we have. 21:24.760 --> 21:30.070 So this is a simply if you try to understand me here we have the B value, which is calculated by the 21:30.340 --> 21:31.810 difference of the means. 21:32.910 --> 21:35.190 And we are finding out the. 21:36.740 --> 21:44.450 Squared of E divided by minus the summation of values divided by and so this is in the similar terms 21:44.450 --> 21:48.260 of what we have in B, but it is a combination of both the values. 21:48.260 --> 21:50.500 So it is slightly complex formula. 21:51.140 --> 21:51.680 So. 21:53.020 --> 21:55.640 But you don't need to remember this entire formula. 21:55.660 --> 22:01.780 All you need to remember is the concept and the assumptions that we have that which do you need to apply 22:01.780 --> 22:07.490 for it and then you will be directly applying the best from the calculator itself. 22:07.750 --> 22:13.750 So you just need to have the values and know which test you need to apply while applying statistics. 22:15.800 --> 22:22.100 So then we will be finding out the values and we have to find out the degrees of freedom. 22:22.340 --> 22:24.110 So what would be the degrees of freedom? 22:25.200 --> 22:31.650 We have this data set and we have this data set, so from the independent test. 22:33.310 --> 22:39.100 We can see the degree of freedom is the doable in minus two. 22:40.040 --> 22:50.080 So the total end will be then less than 20, minus two, which is 18, so the degree of freedom is 18. 22:50.420 --> 22:57.260 So we will go to the detail and from the detail, we will select the alpha level and we will compare 22:57.260 --> 23:05.120 with respect to the alpha level and for the degree of freedom of the alpha level is coming out to be 23:05.120 --> 23:05.690 two point. 23:07.400 --> 23:15.230 So when we compare the calculated value, which is minus one point six nine with the alpha level two 23:15.230 --> 23:22.860 point one, we can see that the calculated value is less than the cutoff value, two point one zero. 23:23.160 --> 23:26.970 Therefore, the P value is greater than zero point five. 23:27.170 --> 23:32.840 And as the P value is greater than the alpha level, we cannot conclude that there is a difference between 23:32.840 --> 23:33.390 the means. 23:34.160 --> 23:40.140 So we cannot say that there is a significant difference between the mean values. 23:40.160 --> 23:45.790 So these values can actually be about the same population. 23:47.150 --> 23:54.140 So we cannot conclude that these are different scenarios if they can be a part of the same population. 23:56.940 --> 24:03.120 Here you can see we have a from the table also in the table, the degree of freedom has been selected 24:03.120 --> 24:08.400 as a beam and we come it to this devalue zero point zero to five. 24:08.820 --> 24:09.990 So here we have. 24:10.900 --> 24:16.230 Two point one zero, which is being compared with minus one point six nine. 24:16.660 --> 24:23.650 So when we compare it with minus one point six, so minus one point six nine, which is somewhat higher 24:23.920 --> 24:26.590 and the actual value is to win something. 24:26.710 --> 24:33.010 So hence it will be in the same region in the middle of the region and it will not be a part of the 24:33.010 --> 24:33.870 critical region. 24:34.180 --> 24:37.660 So we cannot conclude we will have to. 24:39.740 --> 24:43.840 See that all these samples are belonging to the same data. 24:48.730 --> 24:54.750 Next is the pig, the test, so let us understand what this is. 24:55.330 --> 25:03.970 Now we will choose the beer to decide if the two measurements on the same item or person or thing is 25:03.970 --> 25:04.490 being them. 25:05.350 --> 25:12.520 So if the measurement is being done on the same item, that is some a group of people from the same 25:12.520 --> 25:15.630 city are being tested for two different things. 25:17.050 --> 25:25.040 So we should also choose this test if the two items that are being measured with all unique conditions, 25:25.040 --> 25:29.870 so that is a unique condition which is attached to this particular scenario. 25:29.890 --> 25:36.190 So, for example, we might be mentioning the car safety performance in vehicle research and testing 25:36.190 --> 25:37.060 a subject. 25:37.360 --> 25:39.810 The cars do a series of crash test. 25:39.940 --> 25:47.260 So we are applying different crash tests on different cars and we're testing them. 25:47.590 --> 25:54.310 So the null hypothesis for this would be that the meaning of one is equal to the mean of two. 25:54.580 --> 25:58.380 So in other words, it assumes that the means of equal. 25:58.630 --> 26:05.440 So we will be comparing what the means and finding out if they're significantly different, if they 26:05.440 --> 26:11.410 are significantly different than the means would be different and they would be a of two different populations. 26:11.650 --> 26:14.170 So would the bear be the null hypothesis? 26:14.170 --> 26:18.400 Is that the pairwise difference between the two, this is equal to the. 26:22.140 --> 26:29.670 Newly equal to zero, so this is the difference between the independent, somebody based on the their 26:29.670 --> 26:32.310 deepest that is an independent of somebody. 26:32.340 --> 26:42.540 This we we're finding out that if both the means are equal, that is both the means of the two distributions 26:42.540 --> 26:47.650 that we have are equal or not, if they're belonging to the same population or not. 26:48.060 --> 26:54.410 But here what we will be finding out, we will be finding out that we have these two populations. 26:54.630 --> 26:59.390 So for these two populations, that we have different scenarios. 26:59.520 --> 27:01.390 Is there any difference or not? 27:01.560 --> 27:08.730 So if the difference between both of these should be equal and different in the world of finds, these 27:08.730 --> 27:09.870 are being calculated. 27:09.870 --> 27:13.290 We are calculating same thing at two different intervals of time. 27:13.530 --> 27:16.680 We want to prove that there is no impact of dying on this. 27:16.890 --> 27:20.940 So the difference between these two is equal to Z. 27:21.300 --> 27:25.140 This is what we are trying to work on in the field the best. 27:28.320 --> 27:36.060 So here, let us try to calculate the BRT this, so here we have the steps forward, we have these two 27:36.060 --> 27:38.910 schools given for the same subjects. 27:40.170 --> 27:45.610 So the first step is to subtract each white school from the school. 27:45.810 --> 27:54.120 So we will subtract this school from the initial school so we get minus seven B minus and minus 10. 27:54.330 --> 27:56.520 So such that we will get these scores. 27:57.420 --> 28:04.110 The next step is to add all the values from step one, so we add all the values from step one, the 28:04.110 --> 28:06.840 next step is to square the differences. 28:07.050 --> 28:13.410 So we square these differences and put these here and then find the some of these old. 28:15.390 --> 28:23.160 So we find the differences, find the sum of differences, we find the squares of individual differences 28:23.340 --> 28:27.330 and some of the squares of the individual differences. 28:28.770 --> 28:33.920 After this, we will apply all the values which we have retrieved from the previously. 28:35.080 --> 28:40.840 These sums and the squares of the south, we will put these in this particular formula. 28:42.370 --> 28:43.840 I'm calculate dirty. 28:45.650 --> 28:55.550 And again, using the disvalue, we will be able to calculate the value from the so here the number 28:55.550 --> 28:58.660 of values are pointed to 11. 28:59.180 --> 29:02.300 So there are 11 froster values. 29:03.110 --> 29:05.450 So based on. 29:08.690 --> 29:11.930 Fared the best it has to be in minus one. 29:14.100 --> 29:16.890 So the degree of freedom would be in minus one. 29:23.190 --> 29:31.860 So we will put this one in the formula that is 11 minus one and 11, and we will get the value as minus 29:31.860 --> 29:32.860 two point seven four. 29:33.240 --> 29:36.210 And again, we can compare it with the other values. 29:36.420 --> 29:38.610 So minus two point seven for. 29:46.860 --> 29:50.580 So four minus two point seven four we will have. 29:54.210 --> 30:02.490 The value from the detail now using the degree of freedom, we will get the alpha level, so the degree 30:02.490 --> 30:11.670 of freedom as then that the value is to point to do it now, we will compare it with the detailed value 30:11.880 --> 30:17.400 so that they will value has a value to minus two point seventy four. 30:18.430 --> 30:26.050 So they calculated the value is greater than the people value and the level of zero point zero five. 30:26.410 --> 30:29.070 So the P value is less than the alpha value. 30:29.230 --> 30:34.000 So we can reject the null hypothesis that there is no difference between the mean. 30:34.210 --> 30:37.620 So these are having difference between the mean. 30:39.260 --> 30:45.920 So we can easily see that these two belong to two different distributions. 30:52.900 --> 31:00.310 Here we can see the value for the degree of freedom, then we have minus two point something, so the 31:00.310 --> 31:01.870 two point something value. 31:04.390 --> 31:06.580 Which is minus two point seven for. 31:10.050 --> 31:17.730 So the minus two point seven four is less than this level, so we can reject the null hypothesis, the 31:17.730 --> 31:25.200 value is greater than this particular value, hence it falls in the critical region and we can reject 31:25.200 --> 31:26.400 the hypothesis.