Statistical Sciences 2244A/B Chapter Notes - Chapter 20: Confidence Interval, Bias Of An Estimator, Normal Distribution
22 May 2018
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Stats 2244
Chapter 20
CHAPTER 20.1
Two-sample problems: proportions
- We will use notation similar to that used in our study of two-sample t statistics. The groups we
want to compare are Population 1 and Population 2. We have a separate SRS from each
population or responses from two treatments in a randomized comparative experiment
- A subscript shows which group a parameter or statistic describes. Here is our notation:
- We compare the populations by doing inference about the difference p1 − p2 between the
population proportions. The statistic that estimates this difference is the difference between the
two sample proportions, − .
CHAPTER 20.2
The sampling distribution of a difference between proportions
- Facts on whih we rely when conducting inference for the difference bw two population
proportions:
o when the samples, the distribution of − is approximately normal
o the mean of the sampling distribution is , −
▪ the difference bw sample proportions is an unbiased estimator of the difference
between population proportions
o the standard deviation of the distribution is
CHAPTER 20.3
Large-sample confidence intervals for comparing proportions
- to obtain a confidence interval, one option is to replace the population proportions p1 and p2 in
the standard deviation with sample proportions:
- the result is the standard error of the statistic −
- The confidence interval has the same form we saw before: estimate ± z*SEestimate
- Large sample confidence interval for comparing two proportions:
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Document Summary
We will use notation similar to that used in our study of two-sample t statistics. The groups we want to compare are population 1 and population 2. We have a separate srs from each population or responses from two treatments in a randomized comparative experiment. A subscript shows which group a parameter or statistic describes. We compare the populations by doing inference about the difference p1 p2 between the population proportions. The statistic that estimates this difference is the difference between the two sample proportions, The sampling distribution of a difference between proportions. Large-sample confidence intervals for comparing proportions to obtain a confidence interval, one option is to replace the population proportions p1 and p2 in the standard deviation with sample proportions: the result is the standard error of the statistic. The confidence interval has the same form we saw before: estimate z*seestimate.
