WEBVTT 1 00:00:03.330 --> 00:00:04.163 Hello, students. 2 00:00:04.163 --> 00:00:09.020 Welcome to example five, chapter seven. 3 00:00:11.460 --> 00:00:13.830 In this example, we will learn how to perform 4 00:00:13.830 --> 00:00:16.050 hypothesis testing for two sample 5 00:00:16.050 --> 00:00:18.483 independent dichotomous outcome data. 6 00:00:20.040 --> 00:00:25.040 For this problem we will use problem 27 from our textbook. 7 00:00:25.410 --> 00:00:30.240 And the problem states, use the data shown in problem 25 8 00:00:30.240 --> 00:00:33.150 and test if there is a significant difference 9 00:00:33.150 --> 00:00:35.820 in the proportion of diabetic participants 10 00:00:35.820 --> 00:00:37.350 in the placebo group 11 00:00:37.350 --> 00:00:39.930 as compared to the standard drug group. 12 00:00:39.930 --> 00:00:43.290 Use a 5% level of significance. 13 00:00:43.290 --> 00:00:45.630 Now for your convenience, I have copied and pasted 14 00:00:45.630 --> 00:00:50.630 the table here and before we move forward to step one, 15 00:00:51.090 --> 00:00:52.920 I just want to clarify 16 00:00:52.920 --> 00:00:55.440 the two samples here are independent 17 00:00:55.440 --> 00:00:57.840 because we are comparing the placebo group 18 00:00:57.840 --> 00:00:59.403 to the standard drug group. 19 00:01:01.110 --> 00:01:03.630 And because we are evaluating proportion, 20 00:01:03.630 --> 00:01:06.210 the data here is dichotomous 21 00:01:06.210 --> 00:01:10.413 and given the sample size here, we will be using Z test. 22 00:01:12.480 --> 00:01:15.600 Now in step one, we are stating our hypotheses 23 00:01:15.600 --> 00:01:18.843 and we are also determining the level of significance. 24 00:01:19.920 --> 00:01:22.590 The null hypothesis here states that the proportion 25 00:01:22.590 --> 00:01:25.560 of diabetic participants is equal 26 00:01:25.560 --> 00:01:29.643 and the alternative hypothesis states that it is not equal. 27 00:01:31.895 --> 00:01:33.690 In step two, we will be selecting 28 00:01:33.690 --> 00:01:36.280 the appropriate test statistics 29 00:01:38.280 --> 00:01:43.280 and for step three we will be setting up our decision rule 30 00:01:43.320 --> 00:01:45.960 and we will reject the null hypothesis 31 00:01:45.960 --> 00:01:50.497 if our Z calculated is less than or equal to 1.960, 32 00:01:51.720 --> 00:01:54.583 or if our Z calculated is greater than 33 00:01:54.583 --> 00:01:57.780 or equal to 1.960. 34 00:01:57.780 --> 00:02:02.730 Now we will be computing the test statistics. 35 00:02:02.730 --> 00:02:04.830 Now here we will need to calculate 36 00:02:04.830 --> 00:02:07.500 the overall proportion p-hat 37 00:02:07.500 --> 00:02:12.500 and that will be x1 + x2 divided by n1 + n2. 38 00:02:14.160 --> 00:02:16.200 So we get those figures 39 00:02:16.200 --> 00:02:20.190 and we perform the calculation 40 00:02:20.190 --> 00:02:22.803 and our p-hat is 0.3. 41 00:02:24.030 --> 00:02:27.330 Now, when we substitute the values 42 00:02:27.330 --> 00:02:30.720 and we compute our test statistics, 43 00:02:30.720 --> 00:02:34.890 we see that our Z here is 0.49. 44 00:02:34.890 --> 00:02:37.920 Of course, the values here for p1-hat and p2-hat 45 00:02:37.920 --> 00:02:40.440 are provided to us in the table, 46 00:02:40.440 --> 00:02:44.130 and the p-hat is the one we just calculated 47 00:02:44.130 --> 00:02:47.580 and the n1 and the n2 are also provided to us. 48 00:02:47.580 --> 00:02:52.500 So again, once we insert these values into the formula 49 00:02:52.500 --> 00:02:54.450 and we perform the algebra, 50 00:02:54.450 --> 00:02:58.593 we find out that our Z calculated is equal to 0.49. 51 00:03:00.810 --> 00:03:03.690 Now as far as our conclusion is concerned, 52 00:03:03.690 --> 00:03:06.600 here, we will fail to reject the null 53 00:03:06.600 --> 00:03:10.350 because 0.49 is not less than 54 00:03:10.350 --> 00:03:13.810 or equal to negative 1.960 55 00:03:15.090 --> 00:03:20.090 and 0.49 is not greater than or equal to positive 1.960. 56 00:03:22.260 --> 00:03:25.830 Therefore, we do not have statistically significant evidence 57 00:03:25.830 --> 00:03:29.490 at alpha at 0.05 to show 58 00:03:29.490 --> 00:03:31.470 that there is a difference in the proportion 59 00:03:31.470 --> 00:03:34.140 of diabetic participants in the placebo group 60 00:03:34.140 --> 00:03:36.693 as compared to the standard drug group. 61 00:03:37.710 --> 00:03:39.450 Thank you for your time and attention 62 00:03:39.450 --> 00:03:41.200 and I'll see you in the next video.