​Claim: The mean systolic blood pressure of all healthy adults is less than 124 mm Hg. Sample​ data: For 268 healthy​ adults, the mean systolic blood pressure level is 120.07 mm Hg and the standard deviation is 15.51 mm Hg. ​ 

b. Identify the null and alternative hypotheses.

To test the claim about the mean systolic blood pressure of all healthy adults, we will set up our hypotheses as follows:

### Null and Alternative Hypotheses

1. **Null Hypothesis (H₀):** The mean systolic blood pressure of all healthy adults is 124 mm Hg.
   \[
   H₀: \mu = 124
   \]

2. **Alternative Hypothesis (H₁):** The mean systolic blood pressure of all healthy adults is less than 124 mm Hg.
   \[
   H₁: \mu < 124
   \]

In this setup:
- The null hypothesis \(H₀\) assumes there is no difference, meaning the true population mean systolic blood pressure is equal to 124 mm Hg.
- The alternative hypothesis \(H₁\) aligns with the claim that the true mean is less than 124 mm Hg.

Would you like details on performing the hypothesis test itself?

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Here are some related questions to expand your understanding:
1. How do we determine the test statistic for this hypothesis test?
2. What would be the critical value for this test at a 0.05 significance level?
3. How do we interpret the p-value in this context?
4. How does sample size affect the result of this hypothesis test?
5. What does it mean if we fail to reject the null hypothesis in this scenario?

**Tip:** When setting up hypotheses, ensure that the null hypothesis always includes equality (e.g., \(=\), \(\geq\), or \(\leq\)).

Claim: The mean systolic blood pressure of all healthy adults is less than 124 mm Hg. For 268 healthy adults, the mean systolic blood pressure level is 120.07 mm Hg and the standard deviation is 15.51 mm Hg. Identify the null and alternative hypotheses.

Learn about hypothesis testing using the claim that the mean systolic blood pressure of all healthy adults is less than 124 mm Hg. A sample of 268 healthy adults shows a mean of 120.07 mm Hg with a standard deviation of 15.51 mm Hg. This page discusses how to set up null and alternative hypotheses in such cases, ideal for students in Grades 11-12.

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