Prosser Medical Insurance is concerned that the variation in recovery times (measured in weeks) for heart bypass patients at Mercy Hospital differs from the variation in recovery times for similar bypass patients at Langdon Hospital. You take a random sample of 10 recent patients from Mercy and 10 recent patients from Langdon. Recovery times for the Mercy Hospital sample have a variance of 69.7. Recovery times for the Langdon Hospital sample have a variance of 11.8. Assume that recovery times for both populations represented here have a normal distribution.  

a. Test the hypothesis that the variances of the two populations are equal. Use a significance level of 2%.

b. Test a null hypothesis that the Mercy population variance is no greater than the Langdon population variance, against an alternative hypothesis that the Mercy population variance is greater than the Langdon population variance. Use a significance level of 5%.