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 8.1.6a

Chapter 8, Problem 8.1.6a

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.

Light Year Claim: Most adults know that a light year is a measure of distance. Sample data: A Pew Research Center survey of 3278 adults showed that 72% knew that a light year is a measure of distance.

Verified step by step guidance

Step 1: Understand the problem. The claim is that 'most adults know that a light year is a measure of distance.' In statistical terms, 'most' typically means more than 50%. This will guide us in formulating the hypotheses.

Step 2: Express the original claim in symbolic form. Let p represent the proportion of adults who know that a light year is a measure of distance. The claim 'most adults' translates to p > 0.5.

Step 3: Identify the null hypothesis (H0). The null hypothesis is the statement that there is no effect or no difference, and it is often the complement of the claim. Here, H0: p ≤ 0.5.

Step 4: Identify the alternative hypothesis (H1). The alternative hypothesis represents the claim being tested. Since the claim is that 'most adults' know this fact, H1: p > 0.5.

Step 5: Summarize the hypotheses. The null hypothesis is H0: p ≤ 0.5, and the alternative hypothesis is H1: p > 0.5. These hypotheses will be tested using the sample data provided (72% of 3278 adults).

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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 in hypothesis testing. It is often formulated to be tested against an alternative hypothesis. In this context, H0 might state that the proportion of adults who know that a light year is a measure of distance is equal to a certain value, such as 50%.

Alternative Hypothesis (H1)

The alternative hypothesis (H1) represents the statement that there is an effect or a difference, opposing the null hypothesis. It is what researchers aim to support through their data. For the light year claim, H1 could assert that the proportion of adults who understand that a light year measures distance is greater than 50%, reflecting the original claim.

Symbolic Representation

Symbolic representation in statistics involves expressing hypotheses using mathematical symbols. This allows for clear communication of the hypotheses being tested. For example, if p represents the proportion of adults who know what a light year is, the symbolic forms could be H0: p = 0.50 and H1: p > 0.50, succinctly capturing the claims being evaluated.

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Textbook Question

Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

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Textbook Question

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.

a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?

Exercise 16

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Textbook Question

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.

Systolic Blood Pressure Claim: Healthy adults have systolic blood pressure levels with a standard deviation greater than 5 mm Hg. Sample data: Data Set 1 “Body Data” in Appendix B shows that for 300 healthy adults, the systolic blood pressure amounts have a standard deviation of 15.85 mm Hg.

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Textbook Question

Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs

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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.

Number and Proportions

a. Identify the actual number of respondents who rated themselves as above average drivers.

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Textbook Question

Type I Error and Type II Error

a. In general, what is a type I error? In general, what is a type II error?

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