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Chapter 18 Inference about a Population Proportion. Outline. The sample proportion The sampling distribution of Conditions for inference Large-sample confidence intervals for a population proportion Choosing the sample size Significance tests for a proportion. “ p-hat”.

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outline
Outline
  • The sample proportion
  • The sampling distribution of
  • Conditions for inference
  • Large-sample confidence intervals for a population proportion
  • Choosing the sample size
  • Significance tests for a proportion
1 the sample proportion

“p-hat”

1. The Sample proportion
  • The proportion of a population that has some outcome (“success”) is p.
  • The proportion of successes in a sample is measured by the sample proportion:
standard error of
Standard Error of

Since the population proportion p is unknown, the standard deviation of the sample proportion will need to be estimated by substituting for p.

examples
Examples
  • Example 18.4 Estimating risky behavior (Page 476)
  • Example 18.5 Are the conditions met? (Page 476)
  • Exercise 18.8 No confidence interval. (Page 477)
5 accurate c i for a proportion
5. Accurate C.I. for a proportion
  • Example 18.6 (P479) Shaq’s free shows
6 choosing the sample size
6. Choosing the sample size
  • The margin of error in our confidence interval is
  • We may like to choose the sample size n to achieve a certain margin of error.
guess the sample proportion
Guess the sample proportion:
  • Since we don’t know prior to sampling, we will have to use a guess p* for . There are two ways to do this:
    • Use a guess p* based on a pilot study or on past experience.
    • Use p*=0.50 as the guess. This guess is conservative, as it gives a margin of error bigger than the true margin of error. (Conservative)
example
Example
  • Example 18.7 Planning a poll

(Page 482)

examples1
Examples
  • Example 18.8 Is this coin fair?

(Page 484)

  • Example 18.9 Estimating the chance of head (Page 485)