Question

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.) group of answer choices true false

Answer 1

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