Large Sample Test: Rejecting Hypothesis at 5% Significance

[vandanak]

can someone give me hint of how to do this question
If the standard deviation of output per acre from a sample of 34 representative firms producing wheat 83 kg ,is the hypothesis that standard deviation of output per acre of all firms producing wheat is 107 kg rejected at 5% level of significance? (large sample test)

 

[Stephen Tashi]

Has your class covered the F distribution? If so, you are probably meant to square the sample standard deviations to get sample variations and do a hypothesis test on their ratio, as explained by this PDF: http://www.biostat.wisc.edu/~kbroman/teaching/labstat/fourth/notes06.pdf

 

[vandanak]

Thanks got the point.

 

[Stephen Tashi]

Don't thank me too soon! I was just thinking about this again. The (107)^2 is not a sample variance. It is a hypothesized variance. So I think you use a chi-square test.

 

[Stephen Tashi]

For sample size N, ((N-1) s^2)/ sigma^2 is distributed as chi squared with N-1 degrees of freedom. s = sample variance.

The title of your post is "large sample test". I don' have any statistical tables handy, so I don't know if you N is too large for a table.

 

[Stephen Tashi]

I found a recommendation that says for sample sizes > 30 the normal distribution is used to approximate the chi-squared. Compute X^2 = (N-1)s^2/ sigma^2 and find the Z value for a normal random variable from the formula Z = sqrt( 2 X^2) - sqrt(2( N-1)-1 ). The DOC with that info is here:
http://www.google.com/url?sa=t&sour...sg=AFQjCNG1s9D4FjXX12uLL3wWz8MHF4wmHA&cad=rja

 

[ych22]

I think the Chi-squared test is right, according to the engineering statistics handbook at http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm