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.

검증된 단계별 안내

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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주요 개념

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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.