GENERAL MATHEMATICS FINAL EXAM REVIEWER

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Christiel Kim

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  • Hypothesis

    A statement that something is true. A tentative explanation, a claim, or an assertion about people, objects or events.
  • Statistical Hypothesis

    Any assumption or assertion made on the distribution of a population, which is either true or false.
  • Hypothesis

    A statement that something is true. A tentative explanation, a claim, or an assertion about people, objects or events.
  • Hypothesis testing

    A statistical procedure in determining which hypothesis is more acceptable as true or which hypothesis is more likely to be false.
  • Null Hypothesis (Ho)

    Expresses the idea of no existence of relationship or difference between the variables under study. Usually designated by a not or no term.
  • Null Hypothesis

    • There is no significant relationship between the attitude of students towards their subjects and their performance rating at the end of the semester.
  • Statistical Hypothesis

    Any assumption or assertion made on the distribution of a population, which is either true or false.
  • Hypothesis testing

    A statistical procedure in determining which hypothesis is more acceptable as true or which hypothesis is more likely to be false.
  • Alternative Hypothesis (Ha)

    The opposite of the null hypothesis. It states the existence of a relationship or difference.
  • Null Hypothesis (Ho)

    Expresses the idea of no existence of relationship or difference between the variables under study. Usually designated by a not or no term.
  • Alternative Hypothesis

    • There is a significant relationship between the attitude of students towards their subjects and their performance rating at the end of the semester.
  • Type I error

    Rejecting the null hypothesis when in fact the null hypothesis is true.
  • Null Hypothesis

    • There is no significant relationship between the attitude of students towards their subjects and their performance rating at the end of the semester.
  • Type II error

    Failure in rejecting the null hypothesis when in fact the null hypothesis is false.
  • Alternative Hypothesis (Ha)

    The opposite of the null hypothesis. It states the existence of a relationship or difference.
  • One-tailed test

    Used when the alternative hypothesis is directional, meaning the value is either greater than (>) or less than (<) the other measure.
  • Alternative Hypothesis

    • There is a significant relationship between the attitude of students towards their subjects and their performance rating at the end of the semester.
  • Two-tailed test

    Used when the alternative hypothesis is nondirectional, meaning the value of the measures of the same kind is not equal.
  • Type I error

    Rejecting the null hypothesis when in fact the null hypothesis is true.
  • Type II error

    Failure in rejecting the null hypothesis when in fact the null hypothesis is false.
  • Steps in testing hypothesis
    1. Formulate the null and alternative hypothesis.
    2. Identify the level of significance (α) and the appropriate test statistic.
    3. Determine the critical value/tabular value for the test.
    4. Decide whether to accept or reject the null hypothesis.
    5. State the conclusion.
  • One-tailed test

    Used when the alternative hypothesis is directional, meaning the value of the measures is either greater than (>) or less than (<) the other measure.
  • Two-tailed test

    Used when the alternative hypothesis is nondirectional, meaning the value of the measures of the same kind is not equal.
  • Steps in testing hypothesis
    1. Formulate the null and alternative hypothesis.
    2. Identify the level of significance (α) and the appropriate test statistic.
    3. Determine the critical value/tabular value for the test.
    4. Decide whether to accept or reject the null hypothesis.
    5. State the conclusion.
  • Null Hypothesis

    Shows no significant difference between two parameters.
  • Alternative Hypothesis

    Contrary to the null hypothesis.
  • Level of significance (α)
    The degree of significance in which we accept or reject the null hypothesis. The probability of making the wrong decision when the null hypothesis is true. The most common levels are 0.01, 0.05 and 0.10.
    1. Test

    Used when the population standard deviation (σ) is known and sample size n≥ 30.
    1. Test

    Used when the sample standard deviation (s) is known, population standard deviation (σ) is unknown and sample size n < 30.
    1. Test

    Used to compare 2 or more variances.
  • Rejection region (or critical region)

    Reject the null hypothesis.
  • Acceptance region

    Fail to reject the null hypothesis.
  • Critical value

    A point (boundary) on the test distribution that is compared to the test statistic to determine if the null hypothesis would be rejected.
  • Hypothesis testing for population mean
    When the population standard deviation (σ) is known and sample size n≥ 30, the test statistic is z. When the sample standard deviation (s) is known, population standard deviation (σ) is unknown and sample size n < 30, the test statistic is t.
  • Hypothesis testing for population proportions

    The test statistic is z.
  • Analysis of Variance (ANOVA)

    A comparison test used to determine the significant difference among normal population means. Compares the effects of a factor (e.g. brands of coffee, types of retail stores) on a continuous dependent variable.
  • Assumptions in the use of ANOVA:
  • One-way classification ANOVA

    Uses a single factor, fixed effects model.
  • Two-way classification ANOVA

    The test statistic is the F ratio.
  • Formula to solve F ratio in ANOVA
    Total Sum of Squares (TSS)
    2. Sum of Squares Between-Column (SSb)
    3. Sum of Squares Within-Column (SSw)
    4. Mean Sum of Squares Between (MSSb)
    5. Mean Sum of Squares Within (MSSw)
    6. F-value = MSSb / MSSw