Book cover for Stats Data and Models

Stats Data and Models

Richard D. De Veaux, Paul F. Velleman, David E. Bock

ISBN #9780321986498

4th Edition

1,406 Questions

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16,980 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter provides a detailed overview of testing hypotheses about proportions, emphasizing the importance of formulating appropriate null and alternative hypotheses, checking conditions, and using the one-proportion z-test procedure. Key concepts include calculating the standard deviation of the sampling distribution using the null hypothesis value, then computing and interpreting the test statistic and corresponding P-value. Additionally, the decision-making process in hypothesis testing is illustrated through real-life examples such as quality control in manufacturing and evaluating public claims, highlighting the importance of context in choosing one-sided versus two-sided tests.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Analysis of Variance (ANOVA)

A collection of statistical techniques used to compare the means of three or more groups by partitioning total variability into components due to differences among groups (between-group) and within groups.

Example Problems

Example 1

A very large study showed that aspirin reduced the rate of first heart attacks by $44 \%$. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. a) What is the null hypothesis the company will use? b) What is their alternative hypothesis?

Example 2

A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! a) State the null hypothesis for your experiment. b) State the alternative hypothesis.

Example 3

A clinical trial compares the new drug described in Exercise 1 to aspirin. The group using the new drug had somewhat fewer heart attacks than those in the aspirin group. a) The $\mathrm{P}$ -value from the hypothesis test was 0.28 . What do you conclude? b) What would you have concluded if the P-value had been $0.004 ?$

Example 4

The "psychic" friend from Exercise 2 correctly identified more than $25 \%$ of the cards. a) A hypothesis test gave a P-value of 0.014 . What do you conclude? b) What would you conclude if the $\mathrm{P}$ -value had been $0.245 ?$

Example 5

According to the 2010 Census, $16 \%$ of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a random sample of 437 county residents, and found that 44 of those surveyed are of Hispanic origin. a) State the hypotheses. b) Name the model and check appropriate conditions for a hypothesis test. c) Draw and label a sketch, and then calculate the test statistic and P-value. d) State your conclusion.
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Step-by-Step Explanations

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Common Mistakes

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