A factor in determining the usefulness of an examination as ameasure of demonstrated ability is the amount of spread that occursin the grades. If the spread or variation of examination scores isvery small, it usually means that the examination was either toohard or too easy. However, if the variance of scores is moderatelylarge, then there is a definite difference in scores between\"better,\" \"average,\" and \"poorer\" students. A group of attorneys ina Midwest state has been given the task of making up this year'sbar examination for the state. The examination has 500 totalpossible points, and from the history of past examinations, it isknown that a standard deviation of around 60 points is desirable.Of course, too large or too small a standard deviation is not good.The attorneys want to test their examination to see how good it is.A preliminary version of the examination (with slight modificationsto protect the integrity of the real examination) is given to arandom sample of 24 newly graduated law students. Their scores givea sample standard deviation of 63points. Using a 0.01 level ofsignificance, test the claim that the population standard deviationfor the new examination is 60 against the claim that the populationstandard deviation is different from 60.

(a) Find a 99% confidence interval for the populationvariance. (Round your answers to two decimal places.)

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(b) Find a 99% confidence interval for the populationstandard deviation. (Round your answers to two decimalplaces.)

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Let x = age in years of a rural Quebec woman at thetime of her first marriage. In the year 1941, the populationvariance of x was approximately σ² =5.1. Suppose a recent study of age at first marriage for a randomsample of 31 women in rural Quebec gave a sample variances² = 2.9. Use a 5% level of significance totest the claim that the current variance is less than 5.1. Find a90% confidence interval for the population variance.

(a) Find the requested confidence interval for thepopulation variance. (Round your answers to two decimalplaces.)

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