the certain medicine administated to each of 10 patients resulted in the following increases in the blood pressure is 8, 8, 7,5,4,1,0,0-1,-1 can it be concluded that the medicine was responsible for the increases in blood pressure

To determine whether the medicine was responsible for the observed changes in blood pressure, we can perform a hypothesis test. One common approach is to use a **one-sample t-test** to test whether the mean change in blood pressure is significantly different from zero (since a mean of zero would imply no change).

### Steps for hypothesis testing:

1. **Null Hypothesis (\(H_0\))**: The medicine has no effect on blood pressure, i.e., the mean increase in blood pressure is zero (\(\mu = 0\)).
2. **Alternative Hypothesis (\(H_a\))**: The medicine does have an effect on blood pressure, i.e., the mean increase is not zero (\(\mu \neq 0\)).
3. **Data**: The changes in blood pressure for the 10 patients are: \(8, 8, 7, 5, 4, 1, 0, 0, -1, -1\).
4. **Calculate the sample mean** (\(\bar{x}\)) and standard deviation (\(s\)).
5. **Calculate the test statistic**: 
   \[
   t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
   \]
   where \(n = 10\) (number of patients).
6. **Determine the p-value**: Use the t-distribution with \(n-1\) degrees of freedom to calculate the p-value.
7. **Conclusion**: If the p-value is less than a significance level (typically \(\alpha = 0.05\)), we reject the null hypothesis and conclude that the medicine has a significant effect on blood pressure.

Let me calculate the necessary statistics to test the hypothesis.The results of the hypothesis test are as follows:

- **Sample mean**: \( 3.1 \)
- **Sample standard deviation**: \( 3.73 \)
- **t-statistic**: \( 2.63 \)
- **p-value**: \( 0.027 \)

Since the **p-value** (0.027) is less than the significance level of 0.05, we **reject the null hypothesis**. This suggests that the medicine has a statistically significant effect on blood pressure.

### Conclusion:
The data provides enough evidence to conclude that the medicine likely caused a significant increase in blood pressure.

Would you like further details or clarification?

Here are 5 related questions for further exploration:
1. How does sample size affect the reliability of a t-test?
2. What other statistical tests could be used in such a situation?
3. How can we interpret a p-value in hypothesis testing?
4. What are the assumptions behind the one-sample t-test?
5. How can effect size be calculated in this context?

**Tip**: Always check if your data meets the assumptions of normality when performing a t-test.

The certain medicine administered to each of 10 patients resulted in the following increases in blood pressure: 8, 8, 7, 5, 4, 1, 0, 0, -1, -1. Can it be concluded that the medicine was responsible for the increases in blood pressure?

Explore the application of a one-sample t-test to determine if a specific medicine caused significant increases in blood pressure across 10 patients. Key concepts include hypothesis testing, t-statistics, and p-value interpretation. This problem is suitable for undergraduate statistics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation