Understanding Hypothesis Testing: t-tests, ANOVA, and Chi-Square
School
Drexel University**We aren't endorsed by this school
Course
MATH 202
Subject
Statistics
Date
Dec 11, 2024
Pages
2
Uploaded by PresidentEchidna3373
One sample Hypothesis Test=Type I error: occur when we reject HoType II error: fail to reject HoIf p < α: reject the null hypothesisAt α = .05, is a statistically significant decrease from the national rate of 40 percent? At the 5 percent level of significance, is the true mean smallerthan the specification? (lefted-tail)Two sample Hypothesis TestWhen using independent samples to test the difference between two population means, it is desirable but not necessary for the sample sizes to be the same. Thet-test for two samples of paired data with n observations in each group will usendifferences, making it a one-samplet-test.ANOVAANOVA compares severalmeans(although itstest statisticis based on variances).Variation "within" the ANOVA treatments represents random variation Variation "between" the ANOVA treatments represents differences between group meansWhich of the following isnota characteristic of theFdistribution?It is negative whens12is smaller thans22.
In an ANOVA, the SSE (error) sum of squares reflects: the variation that is not explained by the factors.In a one-factor ANOVA, the computed value ofFwill be negative under no circumstances.In a one-factor ANOVA, the total sum of squares is equal to thesum of squares within groups plus the sum of squares between groups.Chi-Square For a chi-square goodness-of-fit test for a uniform distribution with 5 categories, we would use the critical value for 4 degrees of freedom.A chi-square test of independence is a one-tailed test. The reason is that we square the deviations, so the test statistic lies at or above zero.We sometimes combine two row or column categories in a chi-square test when the expected frequencies are less than 5.