CI Conceptual Questions Flashcards
What is the purpose of a confidence interval?
The purpose of a confidence interval is to estimate a parameter and provide a measure of uncertainty in the estimation
giving a plausible range of values for a parameter based on a statistic
What does “confidence” actually mean?
Confidence means a probability/degree
95% of the intervals you construct would contain the true population parameter.
contains the true value of the parameter 95/100
confidence refers to the fact that this is a range of plausible values for the parameter
What type of variability of CIs account for?
sampling variability ( sample size and sample error)
Explain the relationship between confidence level and interval width
Relationship between confidence level and interval width is directly proportional
-When you increase the confidence level (say from 95% to 99%), you’re asking for more certainty that the interval contains the true parameter.
Explain the relationship between sample size and interval width
The relationship between sample size and interval width is inversely proportional:
As the sample size increases, the width of the confidence interval decreases.
larger sample more precise estimates
How do width of CIs using the normal distribution compare to t-distribution CIs for the same confidence level
(CIs) using the normal distribution versus the t-distribution for the same confidence level,
the width of the confidence interval using the t-distribution will typically be wider than that using the normal distribution, especially when the sample size is small
-The t-distribution is used when the population standard deviation is unknown and you are estimating it from the sample, or when the sample size is small. The t-distribution has heavier tails than the normal distribution.
Why do we use the t-distribution when the 𝜎(pop sd) is not known?
-adds extra variability that we have to account for since we are using the mean SD since we dont know the pop mean SD
Explain the 68-95-99.7% Rule
68% of the data falls within 1 standard deviation of the mean, 95% of the data falls within 2 standard deviations of the mean, and 99.7% of the data falls within 3 standard deviations of the mean.
What is a sampling distribution?
A sampling distribution is the distribution of a whole bunch of statistics from many samples ( All with the same sample size)
-Shows us variability
What is the Margin of Error?
A measure of the uncertainty or potential error in an estimate derived from a sample
Briefly explain what the CLT tells us
The Central Limit Theorem (CLT) tells us that, for a large enough sample size, the sampling distribution of the sample mean will be approximately normal (bell-shaped), regardless of the shape of the population distribution. works for meand and proportions
