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Chapter 5 Guide_F10

# Chapter 5 Guide_F10 - AMS 315 Data Analysis Chapter Five...

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AMS 315 Data Analysis Chapter Five Study Guide Inferences about Population Central Values Fall 2010 Context The one sample tests discussed here are a basic tool of statistical analysis. Student’s work developing a practical one-sample test is the foundation of applied statistics. The material of this chapter should be familiar to you from your prerequisite class. Chapter Five 5.1. Introduction This section is introductory. You should review the discussion of the vocabulary of testing a hypothesis. 5.2. Estimation of μ This section specifies the one sample confidence interval for . The formula on page 229 is fundamental, and the values in Table 5.2 are commonly called for in statistics examinations. 5.3. Choosing the sample size for estimating This section gives the solution to the problem of how large the sample size n should be so that the width of the confidence interval for meets a specification. Note the formulaa on page 231. This has great application in opinion sampling. A Bernoulli trail is the correct random variable to use for an opinion survey. The random variable i Y takes the value 1 if respondent i meets a criterion (for example, supports candidate A in an upcoming election) and is 0 otherwise. Then, p Y E i = ) ( , where p is the fraction in the population meeting the criterion, and 25 . 0 ) 1 ( ) var( - = p p Y i . The estimate of p based on a random sample of size n is n n i i Y n Y p = = = 1 ˆ . Now, . 25 . 0 ) 1 ( ) var( n n p p Y n - = Then, a random sample of size 2 2 2 / ) ( 25 . 0 E z n α will have a confidence interval of half-width E or less.

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5.4. A statistical test for μ This section contains the specification of the one sample test of the null hypothesis = ) ( : 0 Y E H when the ) var( Y is explicitly stated in an examination problem. It also contains further basic vocabulary about testing hypotheses. There will be examination
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Chapter 5 Guide_F10 - AMS 315 Data Analysis Chapter Five...

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