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 2 = 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 s² = 3.1. Use a 5% level of significance to test the claim that thecurrent variance is less than 5.1.(a) What is the level of significance?State the null and alternate hypotheses.O Ho: 0² = 5.1; H₁: 0² # 5.1O Ho: 0² = 5.1: H₁: 0² > 5.1O Ho: 0² < 5.1; H₂:0² = 5.1O Ho: 0² = 5.1; H₁:0² < 5.1(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)What are the degrees of freedom?What assumptions are you making about the original distribution?O We assume a normal population distribution.O We assume a binomial population distribution.O We assume a exponential population distribution.O We assume a uniform population distribution.(c) Find or estimate the P-value of the sample test statistic.OP-value > 0.100O 0.050 < P-value < 0.100O 0.025 < P-value < 0.050O 0.010 < P-value < 0.025O 0.005 < P-value < 0.010OP-value < 0.005(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?O Since the P-value > a, we fail to reject the null hypothesis.O Since the P-value > a, we reject the null hypothesis.O Since the P-value ≤ a, we reject the null hypothesis.O Since the P-value ≤ a, we fail to reject the null hypothesis.(e) Interpret your conclusion in the context of the application.O At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.O At the 5% level of significance, there is sufficient evidence to conclude that the variance of age at first marriage is less than 5.1.

It is given that Sample size n = 51 Sample variance s2 = 3.1 Level of significance = 5% Note :…

Answered: current variance is less than 5.1. (a)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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