Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 8, Section 1 (pp. 584-588; up to “Significance test for a single proportion”)

1. For both sample means and sample proportions the true margin of error for a given level C of confidence is z^*s_statistic, where, in the case of (this is supposed to be p-hat, but the browser may not render it very well), s_statistic = s/n^1/2, and in the case of , s_statistic = [p(1 - p)/n]^1/2. Nevertheless, for proportions, you are told to use the standard error SE = [(1 - )/n]^1/2 instead of s, though this only leads to an approximate margin of error (and hence, only to an approximate level C confidence interval). Explain why this approach, though less accurate, leads to a more realistically-computable confidence interval than did our method for sample means presented in Section 6.1.

   
   
   
   
   
   
   
   
   
   
   

2. Under what circumstances is the approximate confidence interval for proportions, described on p. 587, going to be close enough to the true confidence interval to be satisfactory?

   
   
   
   
   
   
   
   

3. We employ confidence intervals because we know that the sample we gather may yield a sample statistic whose value is somewhat different than the population parameter we seek. What sources of error in sampling does this procedure account for?

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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