Confidence Intervals Flashcards
What is the definition of Confidence Intervals?
The range within which you expect the population parameter to be.
It’s estimation is based on the data we have in our sample
A confidence interval is a much more accurate representation of reality
Can you be 100% confident?
no - unless you go through the entire population
What is the Level of Confidence denoted as?
1-alpha (one minus alpha)
it is called the confidence level of the interavl
What is the value range of Alpha
0-1
How is a confidence interval related to a point estimate?
The point estimate is the midpoint of the interval.
What are the two main situations when calculating Confidence Intervals?
When the Population Variance is Known and when it is Unknown
What is the Reliability Factor?
Z alpha / 2
What are different Alpha levels?
Confidence level = 95%
alpha = 5%
Confidence level = 99%
alpha = 1%
What are common Confidence Levels?
90%, 95%, 99%
a = 10%, 5%, 1%
a = 0.1, 0.05, 0.01
What does a 95% Confidence Level mean?
A 95% confidence interval means that you are sure that in 95% of the cases, the true population parameter would fall into the specified interval
Where does the z of alpha come from?
The z-table. The Standard Normal Distribution table
What is a commonly used term for the Z?
critical value
A more narrow confidence interval translates into?
higher uncertainty
There is a tradeoff between the level of confidence and what?
The range of the interval
What is the accepted norm for Confidence Levels?
95%
What is the formula for Standard Error
SE = sample standard deviation / sqrt(n)
What is significant about Student’s T?
It allows you to make inferences through small samples with unknown population variance and applies to a large number of real life situations
What do fatter tails allow for?
Allows for a higher dispersion of variables and there is more uncertainty
What is the formula for calculating the z-statistic Confidence Interval?
mean +- z-stat * std error
The z-statistic is related to what distribution?
The standard normal distribution
The t-statistic is related to what distribution?
Student’s T distribution
What is a degree of freedom in Student T distributions calculated?
degrees of freedom are equal to n-1
At what number of samples should you use the z table instead of the t table?
50
What is the formula to calculate a t-score with unknown variance Confidence Interval?
x-bar (mean) +- tn-1, a/2 * stderror
or
mean +- t-stat * std error
What is the Excel formula for calculating the t-stat
=T.INV.2T(CI ie 0.05, DF)
What is the Excel formula for calculating the z-stat?
=NORMSINV(0.95 probability) probability = 1-(alpha/2)
90% =NORMSINV(0.95) = 1.64
95% =NORMSINV(0.975) = 1.96
99% =NORMSINV(0.995) = 2.58
What do we get when we know the Population Variance?
we get a narrower confidence interval
What do we get when we do not know the Population Variance?
We get a wider confidence interval - a higher level of uncertainty
What is proper statistic for estimating the confidence interval when the population variance in unknown?
The t-statistic
The formula’s z & t determine the span of the confidence interval. What is their special name?
Margin of Error
Getting a smaller margin of error would mean what in relation to the confidence interval?
it would get narrower
What is the difference between dependent and independent samples?
it’s important to know whether your samples are dependent or independent: If the values in one sample affect the values in the other sample, then the samples are dependent. If the values in one sample reveal no information about those of the other sample, then the samples are independent.
What is an example use of dependent samples?
When researching the same sample over time - looking at the same person before and after
When developing medicine
When looking at families - habits of husbands and wives.
Cause and effect
With independent Samples, what 3 cases can we further distinguish?
- When the population variance is known
- When the population variance is unknown but assumed to be equal
- When the population variance is unknown but assumed to be different
What is the Excel formula for calculating confidence intervals for t-stat?
=CONFIDENCE.T()
=CONFIDENCE.T(0.1,$H$16, 10) - 90%
=CONFIDENCE.T(0.05,$H$16, 10) - 95%
=CONFIDENCE.T(0.01,$H$16, 10) - 99%
An increase in the confidence level will result in______.
a wider confidence interval
“Suppose that you want to know the average height of people living in a town with 2,000 residents. You take a sample of 50 inhabitants, measure them, and find that the mean height is 5 feet 9 inches (5’94). In this case, the sample mean is the parameter, the population mean is the estimator, and 5’9” is the estimate.”
Patrick is wrong - the sample mean is the estimator, the population mean is the parameter, and the result of 5’9” is the estimate
Explanation of correct answer:
The parameter is a particular attribute of population, whereas the sample mean is a statistic that estimates some fact about the population. In this case, the sample mean is an estimator of the population mean. The estimate, on the other hand, is a specific value produced by the estimator.
