A Brief Version: Elementary Statistics Ch 8
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| Hypothesis Testing | A decision-making process for evaluating claims about a population.
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| What are the three methods used to test hypotheses? | The traditional method, the P-value method, and the confidence interval method.
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| Statistical Hypothesis | A conjecture about a population parameter. This conjecture may or may not be true.
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| Null Hypothesis (H sub zero) | A statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.
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| Alternative Hypothesis (H sub one) | A statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.
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| Statistical Test | Uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected.
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| Test Value | The numerical value obtained from a statistical test
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| Type I Error | Occurs is you reject the null hypothesis when it is true.
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| Type II Error | Occurs is you do not reject the null hypothesis when it is false.
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| Level of Significance | The maximum probability of committing a type I error. This probability is symbolized by the Greek letter alpha.
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| The probability of committing a type II error is symbolized by: | The Greek letter beta.
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| Critical Value (C.V.) | The value that separates the critical region from the noncritical region.
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| Critical or Reject Region | The range of values of the test value that indicated that there is a significant difference and that the null hypothesis should be rejected.
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| Noncritical or Nonreject Region | The range of values of the test value that indicated that the difference was probably due to chance and that the null hypothesis should not be rejected.
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| One-Tailed Test | Indicates that the null hypothesis should be rejected when the test value is in the critical region on one side of the mean.
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| Depending on the direction of the inequality of the alternative hypothesis, a one-tailed test can be: | A right-tailed test (>) or a left-tailed test (<).
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| Two-Tailed Test | The null hypothesis should be rejected when the test value is in either of the two critical regions (not equal to).
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| What are the steps in solving hypothesis-testing problems (traditional method)? | State the hypothesis and identify the claim. Find the critical value(s) from the appropriate table. Compute the test value. Make the decision to reject or not reject the null hypothesis. Summarize the results.
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| Z Test | A statistical test for the mean of a population. It can be used when n is 30 or more or when the population is normally distributed and sigma is known.
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| P-Value (or probability value) | The probability of getting a sample statistic (such as the mean)or a more extreme sample statistic in the direction of the alternative hypothesis when the null hypothesis is true.
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| What are the steps in solving hypothesis-testing problems (P-value method)? | State the hypothesis and identify the claim. Compute the test value. Find the P-value. Make the decision. Summarize the results.
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| Decision Rule When Using a P-Value | If P-value is less than or equal to alpha, reject the null hypothesis. If P-value is greater than alpha, do not reject the null hypothesis.
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| If P-value is less than or equal to 0.01: | Reject the null hypothesis. The difference is highly significant.
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| If P-value is greater than 0.01 but P-value is less than or equal to 0.05: | Reject the null hypothesis. The difference is significant.
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| If P-value is greater than 0.05 but P-value is less than or equal to 0.10: | Consider the consequences of type I error before rejecting the null hypothesis.
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| If P-value is greater than 0.10: | Do not reject the null hypothesis. The difference is not significant.
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| t-Test | A statistical test for the mean of a population and is used when the population is normally distributed and sigma is unknown.
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| Degrees of Freedom (d.f.) | = n - 1
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| Sample Proportion (P hat) | = X/n
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| q | = p - 1
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| sigma squared = | Population Variance
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| s squared = | Sample Variance
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| X squared = | Chi-Square
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| Assumptions for the Chi-Square Test for a single variance: | The sample must be randomly selected from the population. The population must be normally distributed for the variable under study. The observations must be independent of one another.
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