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 8.1.8a

Chapter 8, Problem 8.1.8a

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.

Verified step by step guidance

Step 1: Understand the problem. The claim is that the standard deviation of systolic blood pressure levels for healthy adults is greater than 5 mm Hg. This is a one-tailed hypothesis test because the claim specifies a direction ('greater than').

Step 2: Express the original claim in symbolic form. Let \( \sigma \) represent the population standard deviation of systolic blood pressure levels. The claim can be written as \( \sigma > 5 \).

Step 3: Define the null hypothesis (H0). The null hypothesis represents the statement of no effect or no difference. In this case, it is the opposite of the claim. Thus, \( H_0: \sigma \leq 5 \).

Step 4: Define the alternative hypothesis (H1). The alternative hypothesis represents the claim being tested. Based on the problem, \( H_1: \sigma > 5 \).

Step 5: Summarize the hypotheses. The null hypothesis is \( H_0: \sigma \leq 5 \), and the alternative hypothesis is \( H_1: \sigma > 5 \). These hypotheses will be tested using the sample data provided (standard deviation of 15.85 mm Hg for 300 healthy 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 typically formulated to be tested against an alternative hypothesis. In this context, H0 would assert that the standard deviation of systolic blood pressure levels in healthy adults is less than or equal to 5 mm Hg.

Alternative Hypothesis (H1)

The alternative hypothesis (H1) represents the claim or effect that researchers aim to support through their data. It is the opposite of the null hypothesis and suggests that there is a significant effect or difference. For the given claim, H1 would state that the standard deviation of systolic blood pressure levels in healthy adults is greater than 5 mm Hg.

Symbolic Representation

Symbolic representation involves expressing hypotheses using mathematical symbols to clarify the statements being tested. For instance, the null hypothesis can be represented as H0: σ ≤ 5 mm Hg, while the alternative hypothesis can be expressed as H1: σ > 5 mm Hg. This notation helps in formalizing the hypotheses for statistical testing.

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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

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

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.

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.

Textbook Question

RESAMPLING

a. In general, what does it mean to “resample” the following data set consisting of wait times (minutes) of customers waiting in line for the Space Mountain ride at Walt Disney World: 50, 25, 75, 35, 50?

Textbook Question

At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.

a. In testing the common belief that the proportion of male babies is equal to 0.512, identify the values of p^ and p.