00:02
Once again, welcome to a new problem.
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This time we're dealing with inferential statistics.
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We're dealing with inferential statistics.
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And when it comes to inferential statistics, we have hypothesis testing.
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We have hypothesis testing.
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And for the most part, we can test hypotheses involving two samples such that the test is the dependent samples t test where the difference of before minus after of means.
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So the difference of means is tested.
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So we're testing the difference between a means.
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When it comes to confidence interval, we can take the average.
01:11
We can take the average.
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So the before and after values, so we take all the difference between these two.
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So if we have a column, let's call it d equals to before minus after.
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And so we're going to get the average, which we're calling d bar, which is sum of d all over n.
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N is the sample size.
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N is the sample size and sum of d is the summation of the differences.
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So we have a summation of the differences.
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So if you want to get the confidence interval, we're going to say.
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Say d by plus minus t, alpha over two degrees of freedom, n minus 1.
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Standard deviation of the differences over radical n.
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We could also think about the test statistic if we're doing a statistical test.
02:31
So the t would be d minus mu -d, all of or rather s d of a radical n where this is the hypothesized population mean difference which for the most part is typically zero and then this is the standard deviation of the difference of the difference of the differences in before and after values and n is the sample size.
03:33
So n happens to be the sample size.
03:36
We're looking at a new problem and in this particular problem, we want to study the impact of an experimental drug on blood pressure, and we have 15 participants who are, randomly selected and the blood pressure is measured in millimeters of mercury before and after values of the treatment are measured so we see what the blood pressure is before treatment and the blood pressure is after treatment we want to determine the 95 % confidence interval for the difference in means that's the first thing we want to do and then the next thing we want to do is to determine if there's an impact of the experimental drug on the blood pressure, we want to see that.
04:29
We want to determine the test statistic.
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We also want to get the distribution of the test statistic under now.
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And of course, we're looking at the p value.
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And besides looking at the p value, remember, we also want to see the conclusion.
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So coming back to the problem, the first part is we want to compute the 95 % confidence interval.
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So d -ba plus minus t alpha over 2 degrees of freedom, n minus 1, s -d over radical n.
05:11
And so if we run the confidence interval for the differences, we're going to get, we're going to to get so we want to do the confidence interval this is t interval i want to call it that and it's a 95 % confidence interval and so we're going to get a d bar is the same as 120 .4667 plus minus the t distribution remember we have a sample size of um um we have a sample size of 15.
06:00
So the degrees of freedom is 15 minus 1, which is 14.
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And at 95 % confidence interval, if we're looking at 14, we're going to get a value of 2 .145 of a radical 15.
06:32
And so the result is equivalent.
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To 114.
06:44
Actually, let me place it right here.
06:51
114 .9 .93 up until 126 .01.
07:01
So 9 .3 and 01.
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So that's what you're seeing right there.
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And then the next part of the problem, this is the second portion of the problem.
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I was saying the requirements is to determine if there's going to be an impact...