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:

IRR

Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. It is used to evaluate the attractiveness of an investment or project.

Hard Capital Rationing

Hard capital rationing involves a situation where a company cannot access additional funds for investments at any cost due to external factors, such as market conditions or regulatory limits.

Discounted Payback

A capital budgeting method that calculates the time it takes to recoup an investment's initial costs, taking the time value of money into account.

Time Value of Money

The concept that money available at the present time is worth more than the same amount in the future due to its earning capacity.