5. Goodness of fit tests - Normal population Aa Aa Manufacturing processes, such

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5. Goodness of fit tests - Normal population Aa Aa Manufacturing processes, such as coin minting, are subject to small variations due to variations in materials, temperature, and humidity. The variations in materials, temperature, and humidity from their norms are just as likely to be positive as negative but are more likely to be small than large. Consider the 1 coin issued by Belgium. Realizing that there are small variations in the minting process and random error in the weighing process, it might be reasonable to assume that the population of coin weights is normally distributed. Let's confront this assumption with sample data and see how it fares. A random sample of 250 Belgian 1 coins was selected. Each of the 250 coins was weighed and its weight (in grams) recorded The sample mean R is 7.510 grams, and the sample standard deviation s is 0.033 grams The questions that follow walk you through the steps of a test of the hypothesis that the population of weights of Belgian 1 coins has a normal distribution with a mean of 7.510 grams (the sample mean) and a standard deviation of 0.033 grams (the sample standard deviation). Note that you are using the sample mean as an estimate of the population mean and the sample standard deviation as an estimate of the population standard deviation. [Data source: A sample of size n = 250 was randomly selected from the sample of size n 2,000 in the Journal of Statistics Education data archive, euroweight.dat data set.) Select a Distribution Distributions 0 1 23

Explanation / Answer

from above given data:

therefore expected frequency for category 3 is (250/10)=25. and the contribution of category 3 to the chi...is =(26-25)2/25 =0.04

the chi square test stat is therefore 8.76+0.04=8.80. and its p value is 0.4559.

the critical value is 21.6660 and the null hypothesis is retained.

please revert for any clarification

category probability observed Expected Chi square O E=total*p =(O-E)^2/E 1 10% 22.000 25.00 0.36 2 10% 35.000 25.00 4.00 3 10% 26.000 25.00 0.04 4 10% 29.000 25.00 0.64 5 10% 26.000 25.00 0.04 6 10% 18.000 25.00 1.96 7 10% 20.000 25.00 1.00 8 10% 22.000 25.00 0.36 9 10% 24.000 25.00 0.04 10 10% 28.000 25.00 0.36 100% 250 250 8.8000

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