6.4: Tests of Variance, Correlation, and Independence

Question 1

Types of test statistics:

1. One population mean:
2. Two population mean:
3. One population variance:
4. Two-population variance:

Answer 1

1 - Use t-statistic or z-statistic
2 - Use t-statistic
3 - Use Chi-square statistic
4 - Use F-statistic

Question 2

Nonparametric test - a test that is…

Answer 2

Not concerned with a parameter or that makes minimal assumptions about the population from which a sample comes.

Question 3

What are the four situations in which we would need to use nonparametric test?

Answer 3

(1) when the data we use do not meet distributional assumptions,
(2) when there are outliers,
(3) when the data are given in ranks or use an ordinal scale, or
(4) when the hypotheses we are addressing do not concern a parameter.

Question 4

In tests concerning the variance of a single normally distributed population, we make use of a…

Answer 4

Chi-square test statistic, denoted χ2.

Question 5

If we have n independent observations from a normally distributed population, the appropriate test statistic is:

Answer 5

X^2 = (n-1)s^2 / σ^2

Question 6

The Spearman rank correlation coefficient is essentially an…

Answer 6

Equivalent to the usual correlation coefficient but is calculated on the ranks of the two variables (say, X and Y) within their respective samples.