Ch. 8 - Hypothesis Testing

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 8 - Hypothesis Testing

Problem 8.1.5

Chapter 8, Problem 8.1.5

Identifying H0 and H1
In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.
b. Identify the null and alternative hypotheses.

Landline Phones Claim: Fewer than 10% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 16,113 homes, 5.8% had landline phones without wireless phones.

Verified step by step guidance

Step 1: Understand the problem. The claim is that fewer than 10% of homes have only a landline telephone and no wireless phone. This is a one-tailed hypothesis test because the claim specifies 'fewer than.'

Step 2: Express the original claim in symbolic form. Let p represent the proportion of homes with only a landline telephone and no wireless phone. The claim can be written as: p < 0.10.

Step 3: Define the null hypothesis (H0). The null hypothesis always includes equality or no effect. In this case, H0: p = 0.10.

Step 4: Define the alternative hypothesis (H1). The alternative hypothesis represents the claim being tested. Here, H1: p < 0.10.

Step 5: Summarize the hypotheses. The null hypothesis (H0) is p = 0.10, and the alternative hypothesis (H1) is p < 0.10. These hypotheses will be tested using the sample data provided.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that 10% or more of homes have only a landline phone. It is the hypothesis that researchers aim to test against, and it is typically assumed true until evidence suggests otherwise.

Alternative Hypothesis (H1)

The alternative hypothesis (H1) represents the statement that there is an effect or a difference, opposing the null hypothesis. In this scenario, it would claim that fewer than 10% of homes have only a landline phone. This hypothesis is what researchers hope to support through their data analysis, indicating a significant finding if the null hypothesis is rejected.

Symbolic Representation

Symbolic representation involves expressing hypotheses using mathematical symbols for clarity and precision. For the given claim, the null hypothesis can be represented as H0: p ≥ 0.10, while the alternative hypothesis can be expressed as H1: p < 0.10, where p denotes the proportion of homes with only a landline phone. This formalization aids in statistical testing and interpretation of results.

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Related Practice

Textbook Question

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In Exercises 9–12, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.)

Exercise 5 “Landline Phones”

Textbook Question

Statistical Literacy and Critical Thinking

In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.

Requirements Are the requirements of the hypothesis test all satisfied? Explain.

Textbook Question

Testing Claims About Variation

In Exercises 5–16, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population.

Pulse Rates of Men A simple random sample of 153 men results in a standard deviation of 11.3 beats per minute (based on Data Set 1 “Body Data” in Appendix B). The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute; see the accompanying StatCrunch display for this test. What do the results indicate about the effectiveness of using the range rule of thumb with the “normal range” from 60 to 100 beats per minute for estimating in this case?

Textbook Question

Testing Claims About Proportions

In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.

Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. Should this be comforting to physicians?

Textbook Question

Testing Claims About Proportions

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Textbook Question

Type I and Type II Errors

In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)

The proportion of drivers who make angry gestures is greater than 0.25.