Six Independent Samples of 100 Values Each Are Randomly Drawn $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 } = \mu _ { 6 }$

question 7

Essay

Six independent samples of 100 values each are randomly drawn from populations that are normally distributed with equal variances. You wish to test the claim that $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 } = \mu _ { 6 }$ .
i) If you test the individual claims $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 1 } = \mu _ { 3 } , \mu _ { 1 } = \mu _ { 4 } , \ldots , \mu _ { 5 } = \mu _ { 6 }$ , how many ways can you pair off the 6 means?
ii) Assume that the tests are independent and that for each test of equality between two means, there is a $0.90$ probability of not making a type I error. If all possible pairs of means are tested for equality, what is the probability of making no type I errors?
iii) If you use analysis of variance to test the claim that $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 } = \mu _ { 6 }$ at the $0.10$ level of significance, what is the probability of not making a type I error?

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Gender Wage Gap

The average difference in earnings between women and men in the workforce, often highlighted as a measure of gender inequality.

Efficiency Wages

A theory suggesting that higher wages can enhance worker productivity by increasing morale, reducing turnover, and attracting more skilled employees.

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The skills, knowledge, and experience possessed by an individual or workforce, viewed in terms of their value or cost to an organization.

Human Capital

Represents the skills, knowledge, and experience possessed by an individual or population, viewed in terms of their value or cost to an organization or country.