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A survey across generations of workers gathered data on engagement at work. The results for a sample of 1,000 workers are in the accompanying contingency table. At the 0.01 level of significance, is there evidence of a significant relationship between generation and level of engagement in the workplace? What are the null and alternative hypotheses to test? H0: _A__ relationship exists between __B__ and __C__. H1: _D__ relationship exists between __E__ and __F__. A and D: A or No B and E: Gen Xers, traditionalist, generation, baby boomer or millennials C and F: being engaged, being actively disengaged, not being engaged or level of engagement

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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A survey across generations of workers gathered data on engagement at work. The results for a sample of 1,000 workers are in the accompanying contingency table. At the 0.01 level of significance, is there evidence of a significant relationship between generation and level of engagement in the workplace?

What are the null and alternative hypotheses to test?

H0: _A__ relationship exists between __B__ and __C__.

H1: _D__ relationship exists between __E__ and __F__.

A and D: A or No

B and E: Gen Xers, traditionalist, generation, baby boomer or millennials

C and F: being engaged, being actively disengaged, not being engaged or level of engagement

Generation and Level of Engagement
GENERATION
LEVEL OF ENGAGEMENT Millennials Gen Xers Baby Boomers Traditionalists Total
Engaged
Not Engaged
Actively Disengaged
Total
105
200
107
144
64
91
13
316
139
16
499
55
58
8.
185
1,000
360
315
288
37
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Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

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