Concept explainers
Most people would agree that increased information should give better predictions. Discuss how sampling distributions actually enable better predictions by providing more information. Examine Theorem 7.1 again. Suppose that x is a random variable with a
What happens to the standard deviation of the
n | 1 | 2 | 3 | 4 | 10 | 50 | 100 |
|
1σ | 0.71σ | 0.58*7 | 0.50σ | 0.32σ | 0.14σ | 0.10σ |
In this case, “increased information" means a larger sample size n. Give a brief explanation as to why a large standard deviation will usually result in poor statistical predictions, whereas a small standard deviation usually results in much better predictions. Since the standard deviation of the sampling distribution
Give the preceding discussion some thought and explain why you should get much better predictions for µ by using
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Chapter 7 Solutions
Understanding Basic Statistics
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