WEBVTT
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We're told that in 2005 12.5% of American workers belong
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to unions. That gives us a proportion of 0.1
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to 5. And we're also told that in 2006
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we want to test to see if the proportion of
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American workers and unions has increased. We're told that
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in 2006 we have a sample of 400 workers for
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Part 80 were asked to formulate a hypothesis test for
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this scenario, so the alternative hypothesis would be that
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proportion is greater than 0.25 and therefore, the no
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hypothesis is that he is less than or equal to
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0.1 to 5, and we can see that this
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is an upper tail a test. So that's our
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hypothesis. Test for B were as to calculate the
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P value for our scenario, and we're told that
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of the 400 workers in the sample, 52 were
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in unions, so that is a sample proportion,
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and that is equal to 0.13 So the next question
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ask ourselves, is how our sample proportions distributed and
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because end times p greater than or equal to five
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this could be verified easily. It's 400 times 0.1
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to 5 and in times one minus P is also
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greater than or equal to five. Therefore, the
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sample proportions are approximately normally distributed, and so we're
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using the said statistic. So for sample proportions is
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that statistic can be estimated by and then plugging in
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the numbers, and that comes out to the 0.3
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. So now for the P value, so 0.3
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would be somewhere around here. And so once we
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look when we look up 0.3 on the table,
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it's going to give us an area that corresponds to
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the cumulative probability, which is the area in the
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chart to the left of the said score. But
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RPI value is the area in the upper tail and
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from the said from the said table were given that
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this area is equal to 0.6179 and therefore the P
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value is equal to one minus 0.6179 So we have
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P value equals one minus 0.6179 in that equals 0.38
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to 1. So that's the P value that that
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ends. Part B and Part C were asked what
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we would conclude if at an Alfa level of 0.5
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So quite simply, a P value is bigger than
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Alfa. Therefore, we fail to reject the null
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hypothesis.