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First we need to test that whether the average weight of the boxes is more than 500 grams or not.
For that we assume that the sample id coming from a Normal Population.
) population. Let us estimate the
Let
be the 100 samples drawn from the (
population mean and population variance be their sample counterpart as defined below,
Sample mean, ̅
We want to test here ∑ and Sample variance, ( ) ∑ ( ̅) against For this test we define a statistic known as Students t statistic as follows,
√ (̅ )
( and we reject the null hypothesis at
̅ ) significance level if we get or in other words if √ From calculation, as shown in the attached excel sheet, we find,
value comes out to be
where as ̅
. and the cut off Thus at
significance level we can reject the null hypothesis, i.e., the average weight of the boxes
of the detergent are definitely more than 500 grams.
(a) Now we have to test the normality of the population which we assumed in the first part
using the ChiSquare Test of goodness of fit.
The test is defined as, let
be the number of observation belonging to each
class defined for the data. And moreover suppose that
be the probabilities of
∑
any observation falling into those classes. Again we define
Then the statistic is defined as,
∑ ( ) We reject the null hypothesis if observed
at
significance level.
After calculation using Excel and R, to be found in the attached files, we find observed
and
Moreover we can define the pvalue as the probability of the rejection region under the null
hypothesis. Alternatively, pvalue is the probability of observing under null hypothesis a
sample outcome at least as extreme as the one observed. The smaller the pvalue the more
extreme the outcome and the stronger the evidence against the null hypothesis.
Here we find the pvalue to be
which is much smaller than
Thus combine both the result we can safely reject the null hypothesis at
significance
level, i.e., the sample is not coming from a Normal Distribution. Hence the manufacturers
claim is not justified. ...
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This note was uploaded on 08/04/2011 for the course ECN 601 taught by Professor Professor during the Spring '10 term at Grand Canyon.
 Spring '10
 Professor
 Economics

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