unit 6 Flashcards
What is the purpose of hypothesis testing on means?
Hypothesis testing on means is used to compare a sample mean to a known or hypothetical population mean.
When is a standard (normal) distribution used in hypothesis testing on means?
A standard (normal) distribution is used when the population variance or standard deviation is known.
When is Student’s t distribution used in hypothesis testing on means?
Student’s t distribution is used when the population variance or standard deviation is unknown.
What are the characteristics of the Student’s t distribution?
The Student’s t distribution is symmetric, ranges from negative infinity to infinity, and has a mathematical expectation (mean) of 0.
What does it mean for a hypothesis to be bidirectional?
A bidirectional hypothesis, also known as a two-tailed test, tests if a sample mean is different from a population mean, without specifying the direction of the difference.
What are the three possible forms of a statistical hypothesis when comparing a sample mean to a population mean?
The three possible forms of a statistical hypothesis are: H0: ത = µ, H1: ത ≠ µ (bidirectional), H0: ത ≥ µ, H1: ത < µ (left-tailed), and H0: ത ≤ µ, H1: ത > µ (right-tailed).
What is the decision rule for a two-tailed test with a known population variance using a z-score?
Reject H0 if Z ≥ z1-𝛂/2 or Z ≤ -z𝛂/2.
What is the decision rule for a one-tailed (left) test with a known population variance using a z-score?
Reject H0 if Z ≤ -z𝛂.
What is the decision rule for a one-tailed (right) test with a known population variance using a z-score?
Reject H0 if Z ≥ z1-𝛂.
How is a test statistic transformed into a probability (p)?
A test statistic (such as a z-score or a t-score) is compared to its respective distribution (standard normal or Student’s t) to obtain a probability of occurrence.
What is the degrees of freedom in a Student’s t-test for one mean?
The degrees of freedom in a Student’s t-test for one mean is N - 1, where N is the sample size.
When is a Student’s t-test used to compare two means?
A Student’s t-test is used when comparing two means, especially when the population variance is unknown or when comparing means from two groups.
What is the homoscedasticity assumption?
The homoscedasticity assumption is that the dispersion (variance) of the two groups being compared should be similar.
What are the two types of samples when comparing two means?
The two types of samples are independent samples (different groups of people) and dependent/related samples (same group measured at different times).
What kind of variables are needed for a Student t-test when comparing two independent samples?
It requires a quantitative variable and a dichotomous categorical variable.
What kind of variables are needed for a Student t-test when comparing two dependent samples?
It requires two related quantitative variables.
How is the difference between sample means (D) calculated?
The difference between sample means (D) is calculated by subtracting the mean of the second sample from the mean of the first sample ( ҧ𝑥1 − ҧ𝑥2).
What are the decision rules for rejecting H0 for a t-test, for the different tail options?
The decision rules for rejecting H0 for a t-test are: Two-tailed: If T ≥ t 1-𝛂/2 or T ≤ t 𝛂/2; Left-tailed: If T ≤ t 𝛂; Right-tailed: If T ≥ t 1- 𝛂.
What is the purpose of the Pearson Chi-Square test?
The Pearson Chi-Square test is used to determine if there is a relationship between two categorical variables.
What does the Pearson Chi-Square test compare?
The Pearson Chi-Square test compares observed frequencies (f o) and expected frequencies (f e) in contingency tables.
What are the requirements of the Pearson Chi-Square test?
The Chi-Square test requires that at least 80% of the cells in the contingency table have an expected frequency of at least 5, and it does not require a normal distribution.
What are the degrees of freedom in a Chi-Square test?
The degrees of freedom in a Chi-Square test are calculated as (number of rows – 1) * (number of columns – 1).
What is the decision rule for the Chi-Square test?
Reject H0 if the calculated X² is greater than the theoretical χ² from the table; otherwise, accept H0.
What is the Pearson correlation coefficient (r) used for?
The Pearson correlation coefficient (r) is used to measure the linear relationship between two quantitative variables.
What is the sampling distribution of the Pearson correlation coefficient?
The sampling distribution of the Pearson correlation coefficient is the Student’s t-distribution.
What are the degrees of freedom for the Student’s t-test when testing Pearson’s r?
The degrees of freedom are N-2 where N is the number of paired observations.
What does it mean if the Pearson correlation coefficient, r, equals zero?
A zero correlation coefficient means there is no linear relationship between the variables.
What does a two-tailed test for Pearson’s r test?
A two-tailed test for Pearson’s r tests whether there is a linear relationship (H1: ≠ 0) or not (H0: = 0).
How do you calculate the t statistic for the Pearson’s r?
The t-statistic for the Pearson’s r is calculated with the formula t = 𝑟 * √𝑁−2 /√1−𝑟2.
What is the decision rule for rejecting the null hypothesis in a Pearson’s r test?
The decision rule for rejecting the null hypothesis in a Pearson’s r test is: Reject H0 if T ≥ t1-α/2 or T ≤ tα/2 (for two-tailed test); T ≤ tα (for left-tailed test); or T ≥ t1-α (for right-tailed test).
