Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ 2 = 5.1. Suppose a recent study of age at first...

Let
x
= age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of
x
was approximately σ²
= 5.1. Suppose a recent study of age at first marriage for a random sample of 51 women in rural Quebec gave a sample variance
s
²
= 2.7. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.