MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:### Hypothesis Testing of Systolic Blood Pressure in Male Executives Aged 35-44
The National Center for Health Statistics reports that the average systolic blood pressure for males aged 35-44 years is 121. The medical director of a large company believes the average systolic blood pressure for male executives aged 35-44 years at his company differs from 121. He selects 81 male executives in this age group to participate in his study. Upon reviewing their medical records, he finds the mean systolic blood pressure of this sample to be 127.2 with a standard deviation of 28. Assume the population distribution is approximately normal. Conduct a hypothesis test at the 0.05 significance level to test this claim.
#### Hypothesis Test Questions:
1. **What is the null hypothesis?**
\( H_0: \mu = 121 \)
2. **What is the alternative hypothesis?**
\( H_1: \mu \neq 121 \)
3. **What is the significance level?**
0.05
4. **What is the value of the test statistic?** Report your answer to two decimal places.
(Calculation required)
5. **What is the p-value?** Report your answer to four decimal places.
(Calculation required)
6. **What is the correct decision?**
(Based on p-value and significance level)
7. **What is the appropriate conclusion?**
(Based on correct decision)
8. **How many of the three conditions/assumptions are met?**
Evaluate based on normality, independence, and random sampling.
9. **What is the probability of a type 1 error?**
0.05
For the detailed steps in the hypothesis testing process:
1. **State the hypotheses**:
- Null Hypothesis (\( H_0 \)): The mean systolic blood pressure of male executives aged 35-44 is 121.
- Alternative Hypothesis (\( H_1 \)): The mean systolic blood pressure of male executives aged 35-44 is not 121.
2. **Set the significance level (\( \alpha \))**:
- Typically, \( \alpha = 0.05 \).
3. **Calculate the test statistic**:
\[
z = \frac{\bar{x} - \mu_0}{
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