SOCECOL 13 Chapter Notes - Chapter 21: Confidence Interval, Confounding, Nicotine
25 May 2018
School
Department
Course
Professor
Jessica Mangold
SE13 Statistics
Professor Wong
5/24/18
Chapter 21: The Role of Confidence Intervals in Research
21.1 Confidence Intervals for Population Means
- The Rule for Sample Means Revisited
- the rule for sample means is
- if numerus samples of the same size are taken, the frequency curve of
means from the various samples will be approx. bell-shaped; the mean of
this collection of sample means will be the same as the mean of the pop.
- the standard deviation will be:
population standard deviation/square root of sample size
- Standard Error of the Mean
- the standard deviation for the possible sample means is called standard
error of the mean (SEM)
- SEM = standard error = population standard deviation/square root of n
- in practice population standard deviation is usually unknown + is
replaced by sample standard deviation computed from the data
- sometimes called estimated standard error when sample version used
- Population v. Sample Standard Deviation & Error
- see example -> slightly different values
- when does rule for sample means apply:
- the population of measurements of interest is bell-shaped + a
random sample of any size is measured
- OR the population of measurements of interest is not bell-shaped,
but a large random sample is measured
- Constructing an Approx. 95% Confidence Interval for a Mean
- in about 95% of all samples, the true population mean will be within 2 standard
errors of the sample mean
- aka if add + subtract 2 standard errors to sample mean, in about 95% of all cases
we will have captured true population mean
- 95% confidence interval for a population mean:
- sample mean +/- 2 standard errors
- where standard error = standard deviation/ square root of n
- formula should only be used if at least 30 observations in the sample
- Constructing a General Confidence Interval for a Mean
- confidence interval for a population mean:
- sample mean +/- multiplier x standard error
- multiplier depends on desired confidence level
- Student’s t distribution (“t-multiplier”) = appropriate multiplier when using
sample standard deviation instead of population standard deviation
- confidence interval formula using t-multiplier only valid under one (or
both) of following conditions:
- original population of measurements is approx. bell-shaped
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Document Summary
The standard deviation will be: population standard deviation/square root of sample size. The standard deviation for the possible sample means is called standard error of the mean (sem) Sem = standard error = population standard deviation/square root of n. In practice population standard deviation is usually unknown + is replaced by sample standard deviation computed from the data. Sometimes called estimated standard error when sample version used. The population of measurements of interest is bell-shaped + a random sample of any size is measured. Or the population of measurements of interest is not bell-shaped, but a large random sample is measured. Population v. sample standard deviation & error. Chapter 21: the role of confidence intervals in research. Constructing a general confidence interval for a mean. When does rule for sample means apply: Sample mean +/- multiplier x standard error. In about 95% of all samples, the true population mean will be within 2 standard errors of the sample mean.
