Foundations
What is a point estimate?
A single value (like a sample mean) that estimates a population parameter
What is a confidence interval?
A range of values used to estimate a population parameter
When do we use the t-distribution instead of the z-distribution?
When σ is unknown
Where do you go in StatCrunch to make a confidence interval?
Stat → T Stats → One Sample
What happens to margin of error as sample size increases?
It decreases
What statistic is typically used as the point estimate for μ?
The sample mean
How is a confidence interval written in terms of point estimate and margin of error?
Point estimate ± margin of error
What is the shape of the t-distribution compared to the z?
Similar but with heavier tails
Which option do you choose if you have raw data?
“With Data”
How do you find sample size needed for a specific margin of error in StatCrunch?
Stat → Z Stats → One Sample → Width/Sample Size
What is a margin of error?
The distance between the point estimate and the bounds of the confidence interval
What does “95% confidence” mean in plain language?
We are 95% confident the true population mean lies within the interval
As sample size increases, what happens to the t-distribution?
It approaches the standard normal
Which option do you choose if you have only summary stats?
“With Summary”
Why does increasing n make the interval more precise?
Because variability decreases
How do you find the point estimate from a CI of (18, 24)?
(18 + 24)/2 = 21
How does increasing confidence level affect the interval width?
The interval gets wider
Why does the t-distribution have more area in the tails?
To account for extra uncertainty from estimating σ
What additional option can you select to visualize the interval?
“Graph”
Correctly interpret this: “95% CI is (36, 44).”
We are 95% confident the true mean lies between 36 and 44
How do you find the margin of error from a CI of (18, 24)?
(24 − 18)/2 = 3
Why does the interval widen as confidence increases?
Because the margin of error increases
What is the center of the t-distribution?
0
What confidence level do you set for a 95% confidence interval?
0.95
What is the width of a confidence interval with lower bound 34 and upper bound 38?
4