Ch. 11 - Goodness-of-Fit and Contingency Tables

Triola - Elementary Statistics 14th Edition

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Triola 14th Edition

Ch. 11 - Goodness-of-Fit and Contingency Tables

Problema 11.2.4

Capitolo 11, Problema 11.2.4

Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.

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Understand the context of the hypothesis test: Determine whether the problem involves testing if a parameter is greater than, less than, or simply different from a specific value. This will guide the choice of tail direction.

Recall the definitions of the types of hypothesis tests: A right-tailed test is used when the alternative hypothesis (H₁) states that the parameter is greater than a specific value. A left-tailed test is used when H₁ states that the parameter is less than a specific value. A two-tailed test is used when H₁ states that the parameter is not equal to a specific value.

Examine the alternative hypothesis (H₁): Identify the inequality sign in H₁. If it uses '>', it is a right-tailed test. If it uses '<', it is a left-tailed test. If it uses '≠', it is a two-tailed test.

Consider the research question or claim being tested: The direction of the test depends on whether the claim is about an increase, a decrease, or simply a difference in the parameter being studied.

Conclude the type of test: Based on the inequality in H₁ and the context of the problem, classify the test as right-tailed, left-tailed, or two-tailed, and explain your reasoning clearly.

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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0 in favor of H1. The outcome helps in understanding if there is enough evidence to support a specific claim about the population.

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06:21

Step 1: Write Hypotheses

One-Tailed vs. Two-Tailed Tests

In hypothesis testing, a one-tailed test evaluates the possibility of the relationship in one direction (either greater than or less than), while a two-tailed test assesses both directions. A right-tailed test looks for evidence that a parameter is greater than a certain value, whereas a left-tailed test checks if it is less. The choice between these tests depends on the research question and the nature of the hypothesis.

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09:27

Difference in Proportions: Hypothesis Tests

Critical Region

The critical region in hypothesis testing is the set of all values of the test statistic that would lead to the rejection of the null hypothesis. For a right-tailed test, this region is located in the upper tail of the distribution, while for a left-tailed test, it is in the lower tail. In a two-tailed test, the critical regions are found in both tails, reflecting the possibility of extreme values in either direction.

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05:50

Critical Values: t-Distribution

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Gender and Eye Color The following table describes the distribution of eye colors reported by male and female statistics students (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Is there sufficient evidence to warrant rejection of the belief that gender and eye color are independent traits? Use a 0.01 significance level.

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Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05?

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In Exercises 5–20, conduct the hypothesis test and provide the test statistic and the P-value and/or critical value, and state the conclusion.

Heights Measured or Reported? A random sample of the last digits of heights (in.) of males from Data Set 4 “Measured and Reported” is summarized in the table below. Use these last digits to determine whether they occur with about the same frequency. Use a 0.05 significance level. Do the corresponding heights appear to be measured or reported?

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