week 13 carmen quiz: t distribution

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

false

tn-1 is a value on the t distribution with ______________________________ n-1.

degrees of freedom

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

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

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?

wider

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

false

Suppose X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What is your decision?

reject ho

Suppose n = 10 and you want the value of t to put in your 95% confidence interval for the mean, where you don't know the population standard deviation. The value of t that you find on the t-table in this case is 2.2622.

true

Suppose X has a normal distribution and you run a hypothesis test with Ho: u = 8 and Ha: u > 8. You collect a random sample of n = 11 values, and you find your test statistic is t = 2.50. What two values does the p-value lie between on the t-table?

.01 < p value < .025

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

s