t-distribution

t-distribution is...

flatter and fatter

sample standard deviation

s

the larger n is...

the closer the t-distribution looks to the z distribution

t-test

used when sigma is not known

t n-1

value on the t-distribution with n-1 degrees of freedom

A confidence interval is narrower if you use t than if you use Z. (Assume all else is the same.)

false

population must have...

a normal distribution or at least symmetric distribution

If you don't know the population standard deviation, what do you use as a substitute in your test statistic?

s

95% confidence intervals based on the t-distribution are generally WIDER than confidence intervals based on the Z-distribution (if everything else stays the same.)

true

The larger n is, the closer the t distribution looks to the Z distribution.

true

The t distribution is taller and thinner (more concentrated around the mean) than the Z distribution.

false

t- distribution: penalty

a value that is usually bigger than z, making the interval wider

Suppose a 95% confidence interval for the mean is (10, 12) when you know the value of the population standard deviation (sigma). If you HAD NOT known the value of sigma, would your confidence interval have been wider, narrower, or the same?

true

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