Chapter 12: Inference for Proportions BY: Lindsey Van Cleave.
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Transcript of Chapter 12: Inference for Proportions BY: Lindsey Van Cleave.
Chapter 12: Inference for Proportions
BY: Lindsey Van Cleave
12.1: Inference For a Population Proportion
• The statistic that estimates the parameter p is the sample proportion:
12.1: Inference For a Population Proportion
• p is an unbiased estimator of the population proportion…
12.1: Inference For a Population Proportion
• The distribution of p can be assumed to be normal if…• 1. The population is at least 10 times the
sample.• 2. np is at least 10• 3. n(1-p) is at least 10
• Is p is found to be normal use the following formula to standardize it
12.1: Inference For a Population Proportion
• To test the null hypothesis H0: p=p0 that the unknown p has a specific value, p0, just replace p by p0 in the z statistic and in checking the values of np and n(1-p).
12.1: Inference For a Population Proportion
• In a confidence interval for p, we have no specific value to substitute. In large samples, p, will be close to p. So we replace p by p in determining the values of np and n(1-p). We also replace the standard deviation by the standard errror of p
12.1: Inference For a Population Proportion
• To determine the sample size n that will yield a level C confidence interval for a population proportion p with a specified margin of error m:
Comparing Two Proportions
• In a two-sample problem we want to compare two populations or the responses to two treatments based on two independent samples.
• We compare the population by doing inference about the difference p1-p2
Comparing Two Proportions
• Standard Deviation:
• Confidence Interval
Comparing Two Proportions
• Don’t worry you can do all of the significance tests in your calculator:
• 1. STAT and then TESTS• #6: 2-PropZTest• Enter info and push calculate• Then there is your correct
response!