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

question 44

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 $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 } = \mu _ { 5 } = \mu _ { 6 }$ .
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 means?
i) 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 probabi making no type I errors?
ii) 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 significan what is the probability of not making a type I error?

---

Definitions:

HDC (Holder in Due Course)

A party possessing a negotiable instrument, like a check, who has taken it in good faith and for value, and thus has certain protections.

Negotiable Instrument

A legal document guaranteeing the payment of a specific amount of money, either on demand or at a set time, with the transferable right to receive the payment.

Thief

An individual who steals property belonging to another, with the intent to permanently deprive the owner of it.

Impliedly Promises

refers to commitments or guarantees that are not explicitly stated but are inferred from actions, circumstances, or the nature of an agreement.