To properly write the null hypothesis and make a decision using the Pearson Chi-square test, I need a bit more context. The null hypothesis generally states that there is no effect or no relationship between the variables being tested. Specifically, for a Pearson Chi-square test, the null hypothesis typically takes the form:

• Null Hypothesis (H₀): There is no association between the categorical variables.

For example, if you are testing whether gender and preference for a certain type of product are independent, the null hypothesis would be:

• H₀: Gender and product preference are independent.

The decision using the Pearson Chi-square test is based on comparing the p-value from the test to your chosen significance level (usually 0.05). The steps generally follow:

1. Calculate the chi-square statistic based on the observed and expected frequencies.
2. Determine the degrees of freedom (df) based on the number of categories involved.
3. Find the p-value corresponding to the chi-square statistic and compare it to your alpha level (significance level).
4. Decision Rule:
   • If the p-value is less than the significance level (e.g., 0.05), reject the null hypothesis.
   • If the p-value is greater than the significance level, fail to reject the null hypothesis.

If you have specific data or a study you're working with, feel free to share, and I can help you run the test and interpret the results.

Would you like more details on how to conduct a Pearson Chi-square test, or do you have any specific data you want to analyze?

Related Questions:

1. What is the formula for calculating the Pearson Chi-square statistic?
2. How do you determine the degrees of freedom for the Chi-square test?
3. What assumptions must be met for a Pearson Chi-square test?
4. What does a significant result in the Chi-square test indicate?
5. How can I use the Chi-square test for larger datasets or contingency tables?

Tip: Always check that your data meets the assumptions of the Chi-square test, such as expected cell frequencies being sufficiently large (usually greater than 5).