S5. Confidence Intervals Flashcards
What is the general form for confidence intervals?
(sample statistic ± a number of s.d. × standard error)
Width of the confidence interval depends on the number of standard errors either side of zero you need to go to cover a fixed probability.
Steps constructing a confidence interval for standardised mean with 95%
Typical values for 90%, 95% and 99% confidence intervals
90: ±1.645 standard errors
95: ±1.96 standard errors
99: ±2.58 standard errors
How does the confidence interval change with confidence level?
Increases with confidence level required.
How does the confidence interval change with the standard error?
Increases with the standard error of the statistic.
How does the confidence interval change with variance?
Increases with the variance of the data.
How does the confidence interval change with sample size?
Decreases as the sample size increases.
If we have a 95% confidence level, what does this tell us?
That in approx. 95% of them, the population parameter lies in their range. Each has a 95% change of covering it.
Right or wrong? “Interpreting confidence intervals in terms of the probabilistic behaviour of the population parameter is wrong.”
Wrong: there is a 95% change that the population parameter lies in the interval [a, b].
Right or wrong? “Interpreting confidence intervals in terms of the probabilistic behaviour of the interval is right”
Right: there is a 95% probability that the interval [a,b] will contain the population parameter.
Confidence interval for a single mean
What is the population parameter and esitmator for standard error of the sampling distribution?
95% confidence interval for a single mean?
Confidence interval for the difference in two indpendent means
What is the population parameter and esitmator for standard error of the sampling distribution?
95% confidence interval for the difference in two independent means
Confidence interval for the difference in two dependent mean (paired data)
What is the population parameter and esitmator for standard error of the sampling distribution?