Checking equal variances

Topic: Confidence intervals · more questions on this topic
‹ Lost hours after a safety programme Sizing a poll ›

Lost working hours averaged 91 per month, with standard deviation 14.1, over 50 months after a safety programme, and 108 per month, with standard deviation 14.3, over the 50 months before. Assuming two independent normal samples, give a 95% confidence interval for \sigma_1^2/\sigma_2^2, using F_{49,49;0.975}=1.762. Does it support pooling?

Worked answer (click to show)

s_1^2/s_2^2=14.1^2/14.3^2=0.972. Both samples have 49 degrees of freedom, so the two F quantiles in the interval are the same, 1.762, and the interval is

\Bigl(\frac{0.972}{1.762},\ 0.972\times1.762\Bigr)=(0.552,\ 1.713).

It contains 1. At the 95% level the data are consistent with equal variances, so pooling is reasonable.