WEBVTT 1 00:00:02.610 --> 00:00:03.600 Hello students, 2 00:00:03.600 --> 00:00:08.220 Again, this is example 3 for our chapter 6. 3 00:00:08.220 --> 00:00:12.480 The example I'm using here is from our book. 4 00:00:12.480 --> 00:00:14.550 It is Problem 22. 5 00:00:14.550 --> 00:00:15.637 The problem here states, 6 00:00:15.637 --> 00:00:18.780 "The incubation period, the time between exposure 7 00:00:18.780 --> 00:00:20.580 and development of symptoms, 8 00:00:20.580 --> 00:00:22.950 has been reported to be different 9 00:00:22.950 --> 00:00:25.353 in older and younger individuals. 10 00:00:26.190 --> 00:00:31.190 One such study compared individuals under 65 years of age 11 00:00:31.440 --> 00:00:35.367 to those 65 years and older and found the following." 12 00:00:36.210 --> 00:00:41.130 So here's the table where the data is reported, 13 00:00:41.130 --> 00:00:43.920 and we have the mean and standard deviation 14 00:00:43.920 --> 00:00:48.540 as per incubation period days also given to us. 15 00:00:48.540 --> 00:00:51.007 And now the question is asking us, 16 00:00:51.007 --> 00:00:54.900 "Compute a 95% confidence interval 17 00:00:54.900 --> 00:00:58.500 and estimate for the difference in mean incubation periods 18 00:00:58.500 --> 00:01:01.320 between younger and older adults. 19 00:01:01.320 --> 00:01:04.080 Is there a statistically significant difference 20 00:01:04.080 --> 00:01:06.780 in mean incubation periods? 21 00:01:06.780 --> 00:01:08.910 Justify your response." 22 00:01:08.910 --> 00:01:12.310 So again, this is an example when I am going to use 23 00:01:13.560 --> 00:01:15.750 the typed response 24 00:01:15.750 --> 00:01:19.470 instead of working the problem by hand. 25 00:01:19.470 --> 00:01:21.630 So the first thing we have to do is select 26 00:01:21.630 --> 00:01:26.630 the correct formula, which is given here. 27 00:01:26.760 --> 00:01:30.720 And once we have selected the correct formula, 28 00:01:30.720 --> 00:01:35.070 we need to look at how we are going to calculate the Sp. 29 00:01:35.070 --> 00:01:38.760 So for the Sp here, I have already, 30 00:01:38.760 --> 00:01:40.500 again, given you the formula 31 00:01:40.500 --> 00:01:43.230 as well as I've shown you the calculation. 32 00:01:43.230 --> 00:01:45.420 But keep in mind, before the Sp, 33 00:01:45.420 --> 00:01:49.530 we needed to look at the ratio of the sample variance 34 00:01:49.530 --> 00:01:51.180 and I calculated there 35 00:01:51.180 --> 00:01:55.740 and I found the sample variance to be 0.61. 36 00:01:55.740 --> 00:01:58.230 So therefore we are calculating the Sp here 37 00:01:58.230 --> 00:02:02.643 given the formula and our Sp here is 0.93. 38 00:02:03.480 --> 00:02:07.080 So here now we are going to insert the values 39 00:02:07.080 --> 00:02:08.310 that were given to us. 40 00:02:08.310 --> 00:02:11.340 So x bar 1 minus x bar 2. 41 00:02:11.340 --> 00:02:14.490 So x bar 1 here is 7.5 42 00:02:14.490 --> 00:02:17.070 and x bar 2 is 11.1. 43 00:02:17.070 --> 00:02:21.870 Then of course we have to obtain the z value, 95%, 44 00:02:21.870 --> 00:02:25.650 which we already have looked up from table 1B 45 00:02:25.650 --> 00:02:27.840 and it is 1.96. 46 00:02:27.840 --> 00:02:31.890 Then the Sp that we just calculated is 0.93. 47 00:02:31.890 --> 00:02:36.810 And then here we have to insert the numbers, 48 00:02:36.810 --> 00:02:39.870 our sample size basically, n1 and n2. 49 00:02:39.870 --> 00:02:44.640 So our n1 is 55 and our n2 is 45. 50 00:02:44.640 --> 00:02:49.640 So when we basically solve this equation algebraically, 51 00:02:49.830 --> 00:02:54.830 we get the value negative 3.6 plus minus 0.37. 52 00:02:56.880 --> 00:02:58.860 And then when we solve that further, 53 00:02:58.860 --> 00:03:03.860 we get minus 4.0 to minus 3.2. 54 00:03:04.320 --> 00:03:05.790 So what does that mean? 55 00:03:05.790 --> 00:03:08.970 That means that we are 95% confident 56 00:03:08.970 --> 00:03:11.970 that the difference in true mean incubation 57 00:03:11.970 --> 00:03:16.710 is anywhere between 3.2 to 4.0 days longer 58 00:03:16.710 --> 00:03:20.403 in older patients as compared to younger patients.