Chapter 23: Inferences About Means

Question 1

Define ‘Student’s t’.

Answer 1

A family of distributions indexed by its degrees of freedom. The t-models are unimodal, symmetric, and bell-shaped, but generally have fatter tails and a narrower centre than the Normal model. As the degrees of freedom increase, t-distributions approach the standard Normal.

Question 2

Define ‘Degrees of freedom for Student’s t-distribution’.

Answer 2

For the application of the t-distribution in this chapter, the degrees of freedom are equal to n-1, where n is the sample size.

Question 3

Define ‘One-sample t-interval for the mean’.

Answer 3

A one-sample t-interval for the population mean is
y-bar ± t(n-1) x SE(y-bar), where SE(y-bar) = s/ sqrt(n)
The critical value t(n-1) depends on the particular confidence level, C, that you specify and on the number of degrees of freedom, n-1.

Question 4

Define ‘One-sample t-test for the mean’.

Answer 4

The one-sided t-test for the mean tests the hypothesis H0: μ = μ0 using the statistic t = (y-bar - μ0) / SE(y-bar) where the standard error of y-bar is SE(y-bar) = s/ sqrt(n).

Question 5

To make inferences using the sample mean, we typically will need to estimate its standard deviation. This standard error is given by ..?

Answer 5

SE(y-bar) = s/ sqrt(n)

Question 6

When we use the SE instead of the SD, the sampling distribution model that allows for the additional uncertainty is …?

Answer 6

Student’s t.

Question 7

What is the ME for the confidence interval for the true mean? The df?

Answer 7

ME = t*(n-1) x SE(y-bar)
df = n-1

Question 8

What are the assumptions and conditions?

Answer 8

• Independence Assumption (Randomization Condition,)

- Normal Population Assumption (Nearly Normal Condition)

Question 9

Talked about Normal being a good approx. when df is larger, >60. Round to smaller df, as more conservative.

Answer 9

Also talked about calculating power and sample size.