To test the claim, we need to set up our null and alternative hypotheses based on the population mean ($\mu$).

Step 1: Define Hypotheses

The hypotheses for this problem can be stated as follows:

• Null Hypothesis ($H_0$): The population mean systolic blood pressure is equal to 120 mm Hg.

  $H_0: \mu = 120$

• Alternative Hypothesis ($H_1$): The population mean systolic blood pressure is greater than 120 mm Hg.

  $H_1: \mu > 120$

Explanation: The null hypothesis $H_0$ represents the status quo or no effect, assuming that the population mean systolic blood pressure is 120 mm Hg. The alternative hypothesis $H_1$ reflects the claim we are testing: whether the population mean is actually greater than 120 mm Hg.

Would you like a detailed breakdown of how to calculate the test statistic and reach a conclusion?

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Related Questions:

1. How do we calculate the test statistic for a hypothesis test concerning the mean?
2. What is the critical value for a one-tailed test at a 0.05 significance level?
3. How do we interpret p-values in hypothesis testing?
4. What assumptions must be met to conduct this hypothesis test on the mean?
5. How does the sample size affect the accuracy of hypothesis testing?

Tip: Remember, in hypothesis testing, a high p-value means there is not enough evidence to reject the null hypothesis, while a low p-value suggests the alternative hypothesis may be valid.