ESTIMATING OF THE POPULATION MEAN WHEN THE POPULATION STANDARD DEVIATION IS KNOWN Flashcards
What is the goal of statistics?
Inferential statistics = using sample statistics to ESTIMATE population parameters (drawing conclusions).
The sample results provide […] of the values of the populations characteristics.
estimates. (whether they are “good”estimates or not, depends on the sampling methods used…)
What is the standard error/ stander error of the mean
A measure of how
representative a sample is likely to be of the population
Point estimation is a form of…
Statistical inference.
What is point estimation? Give an example
Using the data from a sample -> sample statistic -> estimate of a population parameter
EXAMPLES
Sample mean (X avec barre) is the point estimator of the population mean (μ)
s2 (sample variance) is the point estimator of the population variance (σ2)
s of σ
Why are some point estimates referred to as “unbiased estimates” ?
An estimator of a given parameter is said to be unbiased if its expected value is equal to the true value of the parameter (MEAN AND SAMPLE VARIANCE (n-1; degrees of freedom))
- standard deviation is biased
What do you have to take into account when choosing a sample statistic as a point estimate of the value of a population parameter?
That the statistic is an unbiased estimator (mean (x barre) and variance (s2) )
What’s the difference between a point estimator and a point estimate ?
Point estimate = value
Point estimator = type of statistic used (e.g., sample mean)
Do point estimate provide exact values
No. They provide values that might be lower or higher than population value. Which is why we use interval estimates [point estimate +/- margin of error]
Are point estimates only from one sample, or an average of samples
Point estimates are typically calculated from one sample. They are used to estimate a population parameter (like the population mean or population proportion) based on the data from that single sample. Hence sample mean and sample variance, and not mean of the distribution of mean or variances of the distribution of means.
Margin of error tells us what?
It tells us how different the point estimate is from the parameter value. So, in other words, how accurate the point estimate is. If its 10 +/- 1, it means that the parameter value is somewhere between 9 and 11, and that the point estimate is 10.
The […] is the population we want to make inferences about.
The […] is the population from which the sample is actually taken.
Target population and sampled population
What is the general form of an interval estimate of a population mean?
X avec barre ± Margin of Error
What is the difference between an interval estimate and interval limits?
INTERVAL ESTIMATE: A range of values within which the actual value of the population parameter may fall.
INTERVAL LIMITS: The lower and upper values of the interval estimate.
“In our simple random sample of 2000 households, we found the mean (X) income to be $65,000, with a standard deviation (s) of $12,000. Based on these data, we believe that the population mean is somewhere between $64,732 and $65,268.”
What is the point estimate of the population mean, of the population standard deviation, the interval estimate and the lower and upper interval limits for the population mean?
- Point estimate of μ $65,000
- Point estimate of σ $12,000
- Interval estimate of μ $64,732 to $65,268
- Lower and upper interval limits for μ $64,732 and $65,268
What is a confidence interval?
An interval estimate for which there is a specified degree of
certainty that the actual value of the population parameter will fall within the interval.
ex: being 90% confident that pop. mean is between those two values
What does a confidence interval contain that the interval estimate does not?
The confidence level.
In fact the CI contains 3 components: sample statistics (1) +/- level of confidence (2) x standard error (3)
What is the sampling error/estimation error/margin of error?
It’s the level of confidence multiplied by the standard error.
What is the formula of the standard error of the mean?
Standard deviation of a distribution of sample means is the square root of the variance of the distribution of means.
How is the level of confidence represented ? (the symbol)
By a Z score
In both interval estimates and confidence intervals we are measuring …
Accuracy.
MULTIPLE CHOICE QUESTION OF THE TEST:
What are 3 things that affect confidence intervals?
va voir diapo 21
1) sample size :
n augmente, width (of the margin of error) decreases
2) Standard deviation of the population or the sample
if it increases, so does the width of the margin of error
(makes sens a bigger standard deviation = plus de variability)
3) Level of confidence
if z score increases, so does the width of the margin of error
What does it mean to say that the confidence level of a population mean is 95%?
For 95% of such intervals, the sample mean would not differ from
the actual population mean by more than ** your sampling error **
The wider the interval estimate, the more confident you can be that it includes the population mean. But at the cost of what….
A wider interval does give us more confidence that it contains the true population parameter, but it’s at the cost of PRECISION
In other words, we’re more certain that the true population value lies somewhere within this broad range, but we’re less sure about the exact value within that range.
