The management of regional hospital has made substantial...

The management of Regional Hospital has made substantial improvements in their hospital and would like to test and determine whether there has been a significant decrease in the average length of stay of their patients in their hospital. The following data has been accumulated before and after the improvements. At the 5% level, test to determine if there has been a significant reduction in the average length of stay. After Before Sample size 45 58 Mean (in days) 4.6 4.9 Population Standard Deviation .5 .6 Test the following hypotheses. H0: µafter - µbefore ≥ 0 Ha: µafter - µbefore < 0

Transcript

00:01 Now in this video, we are told that a hospital management has put up some systems to reduce the length of stay of patients at their hospital.

00:12 And we are told that the hospital system took data of number of people.

00:21 They took a sample of people after the system has been put in place.

00:25 And the number of people's sample was 45.

00:28 And then we found out that the average length of stay after the system has been put in place was 4 .6 days with a standard deviation of 0 .5.

00:41 Also, before the system was put in place, they sampled, so let's make it before b, they sampled 56 persons, and then the average length of stay before the system was put in place was 4 .9 days where the standard.

00:57 Standard deviation of 0 .55.

01:02 The first tax we are asked to do is to formulate a hypothesis test for this preamble or this information.

01:12 So a, what will be our hypothesis test? our null hypothesis, let's call it h0, will be that the average length of stay after the system was put in place and then the average length of stay before, the system was put in place is the same.

01:32 There is no difference between the length of stay.

01:35 Now, because we want to test that the length of stay after the system was put in place was less, it would be a one -tail test.

01:46 So the alternate hypothesis is that will be that the average length of stay after the system has been put in place should be less than the average let of stay before the system.

01:58 Was put in place.

01:59 So this will be our hypothesis, okay, the alternate and then the now hypothesis.

02:09 The second question, which is the b, is asking us to calculate the test statistic.

02:17 So calculate the test, compute the test statistic.

02:21 Computing test at this for this, let me call my test testes this is z cal.

02:26 Z cal.

02:28 And you are using the zs.

02:29 Test because sample sizes 45 and 56 is way above 30 and therefore we can approximate to normal distribution even if it is not normally distributed using the central limit theorem so this will be a formula so we have z x bar of a x bar of b minus u of a minus mu of b all this will be divided by standard deviation squared of and then standard deviation square before the system was put in place so this is what we will have now if you go back to our now hypothesis if we are giving that mu of a equals mu of b then we can actually also write it to be what mu of a minus mu of b and this will give us zero for us to get this.

03:36 So it means that if we come back to our test statistics here, whatever, what is in this bracket will run up to zero.

03:43 So let's now do our substitution and see what we will get.

03:48 So our z calculated will be 4 .6 minus 4 .9 minus 0 all over square root of 0 .5 squared over 45 plus 0 .55 squared over 56.

04:16 Now if you do it well, then our numerator is actually going to give us negative 0 .3...

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