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 41 women in rural Quebec gave a sample variance s2 = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?2 = 5.1; H1: ?2 > 5.1H0: ?2 < 5.1; H1: ?2 = 5.1 H0: ?2 = 5.1; H1: ?2 < 5.1H0: ?2 = 5.1; H1: ?2 ≠ 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? We assume a normal population distribution.We assume a exponential population distribution. We assume a uniform population distribution.We assume a binomial population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. 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.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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 41 women in rural Quebec gave a sample variance s² = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: ?² = 5.1; H₁: ?² > 5.1H₀: ?² < 5.1; H₁: ?² = 5.1 H₀: ?² = 5.1; H₁: ?² < 5.1H₀: ?² = 5.1; H₁: ?² ≠ 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?

We assume a normal population distribution.We assume a exponential population distribution. We assume a uniform population distribution.We assume a binomial population distribution.

(c)

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

P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d)

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

Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis.

(e)

Interpret your conclusion in the context of the application.

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.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.

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