Sure, let's break down the solution step by step.
### Question (a)
What is the degrees of freedom (df) for this chi-square test?
Solution:
The degrees of freedom in a chi-square test are calculated as the number of categories minus 1.
Here, there are 7 categories (Asion Indian, Chinese, Filipino, Japanese, Korean, Vietnamese, Other).
So,
[tex]\[ df = 7 - 1 = 6 \][/tex]
Answer:
[tex]\[ df = 6 \][/tex]
### Question (b)
What is the chi-square test statistic ([tex]\( \chi^2 \)[/tex])?
Solution:
The chi-square test statistic is calculated using the formula:
[tex]\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \][/tex]
Where [tex]\( O_i \)[/tex] is the observed frequency and [tex]\( E_i \)[/tex] is the expected frequency.
Given that the final calculated chi-square test statistic is [tex]\( \chi^2 = 36848.94 \)[/tex]:
Answer:
[tex]\[ \chi^2 = 36848.94 \][/tex]
### Question (c)
What is the p-value?
Solution:
The p-value corresponds to the chi-square test statistic with the given degrees of freedom. If the p-value is less than 0.01, we write 0.
Given the p-value is [tex]\(0.0\)[/tex]:
Answer:
0
### Question (d)
Do we reject the null hypothesis at [tex]\( \alpha = 0.05 \)[/tex]?
Solution:
To determine whether to reject the null hypothesis, compare the p-value with the significance level [tex]\( \alpha \)[/tex].
Given:
- p-value = 0.0
- [tex]\( \alpha = 0.05 \)[/tex]
Since the p-value (0.0) is less than [tex]\( \alpha \)[/tex] (0.05), we reject the null hypothesis.
Answer:
A. Yes
