Module 8.2: Types Of Hypothesis Tests Flashcards
(21 cards)
What is used for hypothesis tests and determining the critical value concerning the value of a population mean?
t-test or z-test (if sample size is large enough)
A z-test is applicable when the sample size is large, typically n > 30, allowing for the use of the central limit theorem.
What test is used to evaluate the equality of two population means?
t-test
The type of t-test depends on whether the samples are independent or dependent.
How do you test a hypothesis concerning the value of a population variance?
Chi-square test
What test is used to evaluate the equality of two population variances?
F-test
What assumptions must be met for the t-test for differences between means?
Samples must be independent and normally distributed
What is a pooled variance used for in hypothesis testing?
t-test for testing the hypothesis that means of two normally distributed populations are equal with unknown but assumed equal variances
What is the test of the mean of the differences used for?
Paired comparisons test for dependent samples
What are the hypotheses structured for a two-tailed test of a single population variance?
H0: σ2 = σ02 versus Ha: σ2 ≠ σ02
What is the shape of the chi-square distribution as degrees of freedom increase?
Approaches normal distribution
What does the chi-square test compare?
Test statistic χ2 to a critical chi-square value at a given significance level
What is the F-test used for?
Testing the equality of variances of two populations
What is the convention for the F-test regarding variances?
Put the larger variance in the numerator
What are the characteristics of a parametric test?
Relies on assumptions regarding the distribution of the population and specific population parameters
When is a nonparametric test used?
When assumptions of parametric tests can’t be supported or when data are not suitable for parametric tests
What is an example where a nonparametric test is called for?
When the distribution of the random variable does not support a parametric test
What is a runs test used for?
To determine whether data are random
What is the critical value for a two-tailed chi-square test with 30 degrees of freedom at a 5% significance level?
16.791 (lower bound) and 46.979 (upper bound)
What happens to the test statistic value when sample variances are equal in the F-test?
The value of the test statistic is 1
True or False: The chi-square test can have negative values.
False
Fill in the blank: The _______ test is used for hypothesis tests concerning the variance of a normally distributed population.
chi-square
What are the degrees of freedom for the chi-square test?
n - 1
