Confidence intervals Flashcards
What is a confidence interval?
What is a confidence interval?
A confidence interval(/reliability interval) refers to a range of scores for which we are, to a certain extent, confident that our sample contains the real population characteristics. A confidence interval provides a range.
What is a confidence interval?
What are point estimators?
Point estimators are the numbers that result from a sample. Based on these numbers you can make statements about the whole population.
Confidence intervals tell you with how much certainty you can say that the point estimator is correct for the entire population.
Reliability
What are the common values for reliability?
90% (a = 0.10)
95% (a = 0.05)
99% (a = 0.01)
Confidence intervals around the mean
Often when you want to calculate the confidence interval, the standard deviation of the population is not known. What do you do instead?
The standard deviation of the sample (S) is used to estimate the standard deviation of the population and to calculate the confidence interval.
The only difference in the formula is that the ‘σ’ becomes a ‘S’
Confidence intervals around the mean
Example: we draw a sample of 45 to apply the normal distribution and use z-values (n>30). The sample mean is 40 and we know that the standard deviation of the entire population is 4. We now know what the limits within the actual average (the confidence interval for the mean μ)
What are the steps of determining the confidence interval?
- Determine the reliability (usually given in the question)
- Determine the sample standard error (SE) of the mean (μ) using the formula
- Determine based on the % of reliability, how many standard deviations you should be from the average (use the table in the appendix)
- Multiply the critical z-value by the standard error of the mean
- Subtract the found value from the mean
- Add the found value to the mean
- The values found in 5 and 6 are the X% confidence interval for the value of the mean μ.
