SOCECOL 13 Chapter Notes - Chapter 20: Confidence Interval, Standard Deviation, Minitab
25 May 2018
School
Department
Course
Professor
Jessica Mangold
SE13 Statistics
Professor Wong
5/24/18
Chapter 20: Estimating Proportions with Confidence
20.1 Confidence Intervals
- statistical methods are used in situations where only one sample is taken + that sample
is used to make conclusion or inference
- confidence interval = an interval of value computed from sample data that is almost
sure to cover the true population number
- one of most common types of inferences
- most common level of confidence used is 95%
- impossible to construct an interval in which could be 100% confident unless measure
the entire population
- confidence levels = the level of certainty that researchers have; sets percentage of risk
that interval does not actually cover the true value
20.2 Three Examples of Confidence Intervals from the Media
- media often supplies information necessary to construct confidence interval
- sometimes will provide interval directly
- most common reported information that can be used to construct confidence interval is
margin of error
- aka margin of sampling error
- margin of error often reported using +/- symbol
- to construct a 95% confidence interval for a population percentage, simply add +
subtract the margin of error to the sample percentage
20.3 Constructing a Confidence Interval for a Proportion
- Introduction
- easy to construct a confidence interval for the proportion or percentage of the
population who fall into one of the categories
- Converting Between Proportions and Percentages
- proportion of a population with a trait is a # between 0 + 1
- percentage is between 0% + 100%
- same conversion between above can be made to endpoints of confidence interval
- easier to derive formula for confidence interval from population proportion
rather than population percentage
- Developing the Formula for a 95% Confidence Interval
- Introduction
- if numerous samples or repetitions of the same size are taken, the
frequency curve made from proportions from the various samples will be
approx. bell-shaped; the mean will be the true proportion from the pop. +
the standard deviation will be:
- the square root of: (true proportion) x (1-true proportion)/(sample size)
- because possible sample proportions are bell-shaped -> in 95% of all
samples, the sample proportion will fall within 2 stan. dev. of the mean
which is the true proportion for the population
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Document Summary
Statistical methods are used in situations where only one sample is taken + that sample is used to make conclusion or inference. Confidence interval = an interval of value computed from sample data that is almost sure to cover the true population number. Impossible to construct an interval in which could be 100% confident unless measure the entire population. Confidence levels = the level of certainty that researchers have; sets percentage of risk that interval does not actually cover the true value. One of most common types of inferences. Most common level of confidence used is 95% Media often supplies information necessary to construct confidence interval. Most common reported information that can be used to construct confidence interval is margin of error. Margin of error often reported using +/- symbol. To construct a 95% confidence interval for a population percentage, simply add + subtract the margin of error to the sample percentage.
