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Probability distribution using sampling techniques

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1. You know that a probability distribution has a mean of 23.20 and a variance of 2.56. You try four different sampling techniques and get the follow results.

Technique Mean
A 20.7
B 19.5
C 26.0
D 25.7

At the 95 percent confidence level, which (if any) of these results is unlikely to have happened by chance?

2. Ballplayers A and B both earn the same salary in 2007. They negotiate new three-year contracts providing for the following salary increases:

2008 2009 2010
Player A 10% 8% 12%
Player B 12% 10% 8%

Indicate whether each of the following statements is true or false, and explain why.

a. Both players will have the same salary at the end of 2010
b. From the players' perspective, Player B's contract is worth more than Player B's

And, for above 2 problems, explain to your boss the reasoning and explanation of how you derived at the final answer.

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This solution assists with determining probability distribution using different sampling techniques.

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Sampling and Sampling Distributions: Example Problem

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

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