Hypothesis Testing

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Abhinnaa

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An energy company, pursuing the making of green gasoline, starts with biomass in the form of sucrose and converts it into gasoline using catalytic reactions. At one step in a pilot point process, the output includes carbon chains of length 3. Fifteen runs with the same catalyst produces the product volumes (liter)

2.79, 2.88, 2.09, 2.32, 3.51, 3.31, 3.17, 3.62,
2.79, 3.94, 2.34, 3.62, 3.22, 2.80, 2.70

While mean product volume is the prime parameter, it is also important to control variation.
Conduct a test with the intent of showing that the population standard deviation is less than 0.8 litres.
Use a significance level of 0.05.

Could some please help me with this question. I just do not know how to start it off/ what to do.

Thanks.
 
Abhinnaa said:
An energy company, pursuing the making of green gasoline, starts with biomass in the form of sucrose and converts it into gasoline using catalytic reactions. At one step in a pilot point process, the output includes carbon chains of length 3. Fifteen runs with the same catalyst produces the product volumes (liter)

2.79, 2.88, 2.09, 2.32, 3.51, 3.31, 3.17, 3.62,
2.79, 3.94, 2.34, 3.62, 3.22, 2.80, 2.70

While mean product volume is the prime parameter, it is also important to control variation.
Conduct a test with the intent of showing that the population standard deviation is less than 0.8 litres.
Use a significance level of 0.05.

Could some please help me with this question. I just do not know how to start it off/ what to do.

Thanks.
Click to expand...
The only way you can estimate the population standard deviation is to assume that the distribution of your 15 samples is approximately the same as the population. So find mean and std.dev. of the data. I think the std.dev. will be approximately 0.5 L.

Now you need a formula for the standard deviation of your standard deviation. I don't have that formula at my fingertips, but it must be in your notes or text. Find the 0.05 significance as the upper tail (single-sided test). Is 0.8 L above that level?
 
A formula for the standard deviation of my standard deviation? I am confused as to what you mean.
 
Abhinnaa said:
A formula for the standard deviation of my standard deviation? I am confused as to what you mean.
Click to expand...
By now you should have found the standard deviation of the given 15 data, either applying the definition or by entering the data in a calculator or Excel. In any case the result will be used as an estimator of the population standard deviation. But how good of an estimate is it? The data themselves have statistical fluctuations, and when you use them in a calculation those statistical fluctuations propagate to the result. Thus your estimator of the population standard deviation is itself a sample from a statistical distribution. In order to specify a confidence interval you either have to know the standard deviation of that distribution,
OR you need to know the distribution itself.

Have you studied the \(\displaystyle \chi^2\) distribution?
 
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