6.3: Mean Differences and Difference in Means

Question 1

For hypothesis tests concerning the population mean of a normally distributed population with unknown variance, the theoretically correct test statistic is…

Answer 1

The t-statistic.

Question 2

Given at least approximate normality, the t-distributed test statistic is always called for when we deal with…

Answer 2

Small samples and do not know the population variance.

Question 3

Formula for calculating T-statistic:

Answer 3

T = x̄ - µ0 / s/√n

Question 4

Which test statistic do we use when the sample is large?

Answer 4

Z-statistic

Question 5

When we want to conduct tests on two means based on samples that we believe are dependent, we use…

Answer 5

The test of the mean of the differences.

Question 6

What is the first step towards test of the mean of the differences (formula):

Answer 6

We begin by calculating dbar , the sample mean difference, di:

1) Dbar = 1/n Σdi

Where n is the number of pairs of observations.

Question 7

What is the second step towards test of the mean of the differences (formula):

Answer 7

When we have data consisting of paired observations from samples generated by normally distributed populations with unknown variances, the t-distributed test statistic is:

T = dbar - µd0 / Sdbar

with n − 1 degrees of freedom, where n is the number of paired observations.