Question 1: True
Question 2: False
Question 1: True
When the population standard deviation (σ) is unknown, the sample standard deviation (s) is used to estimate σ.
However, using s in place of σ introduces some variability into the calculation of the standard error, which in turn affects the width of the confidence interval.
To account for this variability, a t-distribution is used instead of a normal distribution, and the t-statistic is used instead of the Z-statistic.
Question 2: False
A confidence interval is wider if you use t than if you use Z.
This is because the t-distribution has heavier tails than the z-distribution, which means that it is more likely to produce larger t-scores than z-scores for the same sample data.
The wider confidence interval reflects the greater uncertainty about the population mean when you don't know the value of σ.
Question
Question 1
You must use a t instead of a Z in your confidence interval formula for a mean when you don't know the value of sigma. (Assume you have a normal distribution.)
True
False
Question 2
A confidence interval is narrower if you use t than if you use Z. (Assume all else is the same.)
True
False