00:01
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 two branches.
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We have hypotheses testing.
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And we have confidence intervals.
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So we have both hypothesis testing and we also have confidence interval.
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When it comes to hypothesis testing, we can have a normal approximation.
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We can have a normal approximation to a binomial distribution.
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We can have a normal approximation to a binomial distribution.
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And the requirements are that for that to happen, we're going to take the sample size.
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So n is the sample size.
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And then p is the probability of success.
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And of course, q is the probability.
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Probability of failure.
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So we have probability of success and probability of failure.
01:48
And so the mean, there is a requirement that np has to be greater than 5 and n1 minus p also has to be greater than five.
02:05
So those are the two requirements that you're looking at.
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And the problem, you know, we have to figure out if the basics of normal distributions are met.
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So they have to be greater than five for you to use normal approximations, to use normal approximations.
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To a binomial distribution, normal approximations to a binomial distributions.
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And then also, once we've figured out that step, the next step that you're looking at is to find the mean.
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So the mean of the distribution is mu equals to n times p.
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And the standard deviation of the distribution, the standard deviation of the distribution sigma is radical np1 minus p.
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Radical np1 minus p.
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So that's how you're going to get the normal approximation.
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And then, of course, after that, you know, you can run the hypothesis.
03:41
So we can have continuity corrections also.
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And in terms of continuity corrections, if you're thinking about, say, we're thinking about a typical probability problem.
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We're thinking about a typical probability problem that involves, say, the probability, the probability, the probability, the probability that x is less than or equal to n for example.
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So probability that x is less than or equal to n and we want to do a continuity correction for that type of problem.
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So in that case, we're going to say that this is the same as the probability that x the probability that x is less than n plus 0 .05 so that's the relationship that you're looking for right there so x is less than 0 .05 and so so the next step would be to based off of these probability numbers, you know, once you've run the continuity correction, you know, you're going to have to get the z values to dealing with because you're running a normal approximation in this sense...