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

question 13

Essay

Four 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 $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 }$ i) If you test the individual claims $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 1 } = \mu _ { 3 } , \mu _ { 1 } = \mu _ { 4 } , \ldots , \mu _ { 3 } = \mu _ { 4 }$ , how many ways can you pair off
the 4 means?
ii) Assume that the tests are independent and that for each test of equality between two means, there is a 0.99
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 $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 }$ at the 0.01 level of significance, what
is the probability of not making a type I error?

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Definitions:

Change in Price

A variation in the cost of a good or service over a period which can affect demand and supply dynamics in the market.

Price of X

The amount of money required to purchase a specified good or service, indicated here as "X."

Buyer's Budget

The total amount of money that a consumer is willing and able to spend on goods and services within a certain period.

Indifference Curve

A graph representing different bundles of goods between which a consumer is indifferent, showing preferences in terms of trade-offs.