https://file.aiquickdraw.com/mathbot/file/1728377494776coo0fbzd.jpg

For part (a) of this problem, the correct null hypothesis tests whether migraine pain relief is independent of receiving acupuncture. This is because the study aims to determine if receiving acupuncture has an effect on migraine pain relief compared to the control (placebo) group. So, the correct null hypothesis is:

**\( H_0 \): Migraine pain relief is independent of receiving acupuncture.**

For part (b), we are asked to calculate the expected values for the contingency table. These values are calculated based on the formula for expected counts in a contingency table:

\[
\text{Expected Value} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}
\]

Now, let’s compute the expected values for each cell of the table:

1. **Treatment, Pain Free (Yes)**: 
\[
\frac{(62 \times 20)}{157} = 7.90
\]

2. **Control, Pain Free (Yes)**: 
\[
\frac{(95 \times 20)}{157} = 12.10
\]

3. **Treatment, Pain Free (No)**: 
\[
\frac{(62 \times 137)}{157} = 54.10
\]

4. **Control, Pain Free (No)**: 
\[
\frac{(95 \times 137)}{157} = 82.90
\]

These are the expected values, rounded to two decimal places:

- **Treatment, Pain Free (Yes): 7.90**
- **Control, Pain Free (Yes): 12.10**
- **Treatment, Pain Free (No): 54.10**
- **Control, Pain Free (No): 82.90**

Let me know if you need further details or have any questions!

Here are 5 related questions to expand this information:
1. How do we calculate the test statistic for a Chi-square test?
2. What are the degrees of freedom for this test?
3. How do we interpret the results of the Chi-square test?
4. What assumptions need to be met for this test to be valid?
5. How do you reject or fail to reject the null hypothesis?

**Tip:** Always ensure the total of your expected values matches the actual totals in the table when checking your calculations.

Researchers conducted a study to determine if acupuncture relieves migraine pain by randomly assigning 157 patients into treatment and control groups. The table shows the number of patients who were pain-free after treatment and control. Test if migraine pain relief is dependent on receiving acupuncture. Use α = 0.05.

This problem involves a chi-square test for independence to determine if acupuncture affects migraine pain relief. Given a contingency table of treatment and control groups, calculate expected values and interpret the results using hypothesis testing with α = 0.05.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation