7166560 - 43 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

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Unformatted text preview: 43. 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 counter-part 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 Chi-Square 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 p-value as the probability of the rejection region under the null hypothesis. Alternatively, p-value is the probability of observing under null hypothesis a sample outcome at least as extreme as the one observed. The smaller the p-value the more extreme the outcome and the stronger the evidence against the null hypothesis. Here we find the p-value 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.

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