Lecture 4
Lecture: Confidence Intervals
What will I learn? What should I know?
- Understand the term “point estimate”
- Understand the central limit theorem and its core consequence:
that the mean of a data set can be seen as a sample of a normal distribution
always, if the data are sampled from a normal population distribution
also when the data are sampled from a non-normal population distribution, if n is
sufficiently high
- Understand the difference and relation between a standard error and a standard deviation
- Understand the calculation and meaning of a confidence interval
- Understand the similarities and differences between statistical tests and confidence intervals
The process of null hypothesis testing
Inferential statistics:
1. A statistical test: procedure to decide whether a hypothesis about the population may or
may not be supported by the results of the sample
2. Confidence intervals: Check whether the hypothesized parameter falls in an interval around
the sample estimate of which we are very confident that it contains the population
parameter, estimate that we are interested in. also tells us which interval we are confident in
Inferential statistics
- Sample
Sample Mean
Sample proportion
Sample estimate
Sample standard deviation
- Population
Population parameter
Population standard deviation
Unknown
Statistical test
Test Statistic =
- (point estimate –expected value)/SE
- p-value
- H0: reject or retain
Lecture: Confidence Intervals
What will I learn? What should I know?
- Understand the term “point estimate”
- Understand the central limit theorem and its core consequence:
that the mean of a data set can be seen as a sample of a normal distribution
always, if the data are sampled from a normal population distribution
also when the data are sampled from a non-normal population distribution, if n is
sufficiently high
- Understand the difference and relation between a standard error and a standard deviation
- Understand the calculation and meaning of a confidence interval
- Understand the similarities and differences between statistical tests and confidence intervals
The process of null hypothesis testing
Inferential statistics:
1. A statistical test: procedure to decide whether a hypothesis about the population may or
may not be supported by the results of the sample
2. Confidence intervals: Check whether the hypothesized parameter falls in an interval around
the sample estimate of which we are very confident that it contains the population
parameter, estimate that we are interested in. also tells us which interval we are confident in
Inferential statistics
- Sample
Sample Mean
Sample proportion
Sample estimate
Sample standard deviation
- Population
Population parameter
Population standard deviation
Unknown
Statistical test
Test Statistic =
- (point estimate –expected value)/SE
- p-value
- H0: reject or retain
