Lecture 5B: Introduction to Inferential Statistics Flashcards
What is sampling error?
The risk of making errors in estimation because you are not measuring the whole population.
It leads to underestimation or overestimation of the true population mean.
What is the Central Limit Theorem?
the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough
This holds true even if the original population distribution is not normal.
How can you reduce sampling error?
Increase the sample size
(more representative of the population)
A larger sample size decreases the probability that the sample mean is far from the true population mean.
What does the standard error of the mean (SEM) represent?
The standard deviation of the sampling distribution.
SEM is calculated as SD divided by the square root of the sample size.
What is the confidence interval (CI)?
Defines the range of
values within which includes the sample mean
What is a 95% confidence interval (CI)?
95% confidence that the true population mean is within the range defined
by the 95%CI
It is calculated as sample mean ± 1.96(SEM).
True or False: Inferential statistics allows for 100% confidence in conclusions drawn from a sample.
False.
No statistical inference can be made with 100% confidence.
What is a z-score?
A measure of how many standard deviations an element is from the mean.
Z = (x - mean) / SD.
What is the relationship between sample size and 95% CI?
Smaller sample size results in a wider 95% CI.
A larger sample size leads to a narrower CI, indicating more accurate estimation.
Fill in the blank: The formula for calculating SEM is SEM = _______.
SD/√n
What does a p-value represent in inferential statistics?
The probability of making an error when making an inference.
It is used to determine the significance of results.
What happens to the mean of the sampling distribution as the number of samples approaches infinity?
It approaches the true population mean.
This is a theoretical concept described by the Central Limit Theorem.
What is the significance of the area under the standard normal distribution curve?
- area under the entire curve= the total probability of 1 or 100%
- area between two z-scores=probability of obtaining a score within that range
Fill in the blank: The confidence interval is constructed using the formula 95%CI = sample mean ± 1.96(______)
SEM
What does a z-score of +1 indicate?
The score is 1 standard deviation above the mean.
What type of distribution is formed when raw scores are transformed into z-scores?
Standard normal distribution.
The shape of the distribution remains unchanged during this transformation.
What is the primary purpose of inferential statistics?
To make inferences about the properties of a population from a sample.
It is used to test research hypotheses and generalize results.
