Statistics Chapter 8 (Confidence Intervals) Flashcards
What’s a point estimate
A single number that estimates the population
Basically a sample is a point estimate
“0.15 percent of people smoked weed once”
What is a Interval estimate
A range of numbers that estimate the population proportion.
The width of the interval and it’s point estimate is called marigin error.
“ Because of our point estimate of 0.15 we estimate our interval estimate between 0.1 and 0.2, which means there is a marigin error of 0.05.”1
What 2 things make a good point estimater
- It is unbiased (the estimator should not be systematically wrong) the mean of the data should be the same as the population mean
- Small Standart deviation (it should not be imprecise)
What is a confidence interval and the confidence level
The confidence interval is The interval which contains the most believable values for a parameter. This is a range of two numbers.
The confidence level is the probability that this method produces an interval that contains the parameter. This is percentage close to 1 (mostly 0.95)
What affects the margin of error
- The confidence interval (percentage of samples)
2. Sample size n (^2)
What is the interpretation of confidence interval
A 95 % confidence Interval means that in the long run 95% of your confidence intervals will include the true parameter value
It is not that the percentage that the population parameter lies in the confidence interval is 95%
What is the margin of error
It measures how accurate the point estimate is likely to be in estimating the actual value. Like the z value, it is expressed in number of standard deviations from the mean.
In that sense it is the confident interval /2
How do find a confidence interval for 95%
- You take the point estimate of the sample
- You find the margin of error (find standard deviations 95% of data ranges to = 1.96)
- You add and subtract the margin of error to the point estimate
What is the Standart error
It is actually the standard deviation, but the difference is that it is not calculated with a parameter value, but with a eastimated value p (hat).
What 2 things have to be right for confident interval to work
- Data must be obtained by randomization
2. The sample size must be large enough that successes and failures are both at least 15n, so that it is normal
What does it mean when a statistical method is robust?
It is robust if it performs accurately even when the a particular assumption is violated
the t distribution works adequatly even when the data is not completely normaly distributed
What is the t value and why does it exist
The t value substitutes the z value if the sample size is below 30. In that case the standard error becomes easily distorted.
In the table B it is possible to look up values for t by calculating df = n - 1, this is then a new proportion for the z value
If df is over 30, it becomes approximately normaly distributed, which is why it is then similar to z.
How do you calculate the sample size which is fitting for a study with population porportion
- Choose a margin of error (the range of the interval)
- Choose confidence interval
- Solve the formula for n (if p(hat) isnt given choose p(hat) = 0.5)
How do you calculate the sample size which is fitting for a study with population mean
- Choose a margin of error (range of the interval which is its precision)
- Choose confidence interval (how sure you want to be)
- Solve the formular for n (find a pausible standard deviation)
What 4 factors influence sample size n for a study
- Precision (margin of error m)
- Confidence error (z or t score)
- Variation (standard deviation s)
- Cost (how much effort a study is worth)
