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 8.2.1a

Chapter 8, Problem 8.2.1a

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.

Verified step by step guidance

Step 1: Understand the problem. We are tasked with identifying the actual number of respondents who rated themselves as above average drivers. The survey provides the total number of respondents (1020) and the percentage of those who rated themselves as above average drivers (86%).

Step 2: Convert the percentage into a decimal. To do this, divide the percentage (86%) by 100. This gives the proportion of respondents who rated themselves as above average drivers.

Step 3: Multiply the total number of respondents (1020) by the decimal proportion obtained in Step 2. This will give the actual number of respondents who rated themselves as above average drivers.

Step 4: Write the formula for clarity: Actual number = Total respondents × Proportion. Substitute the values: Actual number = 1020 × (86/100).

Step 5: Perform the multiplication to find the actual number of respondents. This will give the final result, which represents the number of adults who rated themselves as above average drivers.

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Key Concepts

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

Simple Random Sample

A simple random sample is a subset of individuals chosen from a larger population, where each individual has an equal chance of being selected. This method ensures that the sample is representative of the population, minimizing bias and allowing for valid statistical inferences. In this context, the sample of 1020 adults provides a basis for analyzing the self-assessment of driving skills among the general adult population.

Proportion

A proportion is a statistical measure that represents the part of a whole, expressed as a fraction or percentage. In this case, 86% of the respondents rated themselves as above average drivers, which can be converted into a proportion by dividing the number of respondents who rated themselves as such by the total number of respondents. Understanding proportions is essential for interpreting survey results and making comparisons.

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence to support a specific claim about a population parameter. In this scenario, the claim is that more than 3/4 (or 75%) of adults consider themselves above average drivers. By conducting a hypothesis test, we can evaluate this claim using the sample data and assess whether the observed proportion significantly exceeds the hypothesized value.

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06:21

Step 1: Write Hypotheses

Related Practice

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

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 15

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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.

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.

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