Question

A researcher wants to ensure the reliability of their EEG set. To do so, they measured impedance in 32 electrodes and found a variance of 62.2 microsiemens. Does this researcher have reason to believe at alpha = 0.05 that the impedance in their electrode set has a variance different than 50 microsiemens?

Answer 1

Data:      

n = 32     

σ^2 = 50     

s^2 = 62.2     

Hypotheses:      

Ho: σ^2 = 50     

Ha: σ^2 ≠ 50     

Decision Rule:      

Degrees of freedom = n - 1 =    32 - 1 = 31

α = 0.05     

Left critical value =   17.53873879    

Right critical value =   48.23188958    

Reject Ho if the test χ2 value <    17.53873879 or > 48.23188958

Test Statistic:      

χ2 = (n - 1) s^2 / σ ^2 =   (32 - 1) * 62.2 / 50 = 38.564   

Decision (in terms of the hypotheses):      

Since 17.53873879 < 38.564 < 48.23188958 we do not reject Ho

Conclusion (in terms of the problem):      

There is no sufficient evidence that the population variance is different from 50 microsiemens.

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