The following problem is based on information from an article by N. Key­tz in the American Journal of Sociology (Vol. 53, pp. 470–480). Let x 5 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 s² = 5.1. Suppose a recent study of age at fi­rst marriage for a random sample of 41 women in rural Quebec gave a sample variance s² = 3.3. 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?

Please provide the following information.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?

(c) Find or estimate the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

(e) Interpret your conclusion in the context of the application.

(f) Find the requested confi­dence interval for the population variance or population standard deviation. Interpret the results in the context of the application.