Systolic blood pressure levels above 120 mm Hg are considered to be high. For the 100 systolic blood pressure levels listed in the accompanying data​ set, the mean is 124.10000 mm Hg and the standard deviation is 16.53738 mm Hg. Assume that a simple random sample has been selected Use a 0.05 significance level to test the claim that the sample is from a population with a mean greater than 120 mm Hg. Click the icon to view the data set of systolic blood pressure levels. Question content area bottom

Part 1 Identify the null and alternative hypotheses.

Upper H 0H0​: 

▼sigmaσ muμ pp

▼not equals≠ greater than> less than< equals=

enter your response here Upper H 1H1​: 

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.

Systolic blood pressure levels above 120 mm Hg are considered to be high. For the 100 systolic blood pressure levels listed in the accompanying data set, the mean is 124.10000 mm Hg and the standard deviation is 16.53738 mm Hg. Assume that a simple random sample has been selected. Use a 0.05 significance level to test the claim that the sample is from a population with a mean greater than 120 mm Hg.

Explore hypothesis testing of systolic blood pressure levels to test if the mean is greater than 120 mm Hg. Using a sample mean of 124.1 mm Hg, a standard deviation of 16.53738 mm Hg, and a 0.05 significance level, this page covers the null and alternative hypotheses and the steps involved in a one-sample Z-test.

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