Question

If population variance is 14.8, sample variance is 15.4 and the number of degrees of freedom is 10, then Chi-square value is __________________ (round off to 2 decimal places).

Hint:

The Chi-square statistic can be calculated using the formula: \(\chi^2 = \frac{(n-1)s^2}{\sigma^2}\).

Answer 1

Correct Answer: 10.38

The formula for the Chi-square statistic is: \[ \chi^2 = \frac{(n-1)s^2}{\sigma^2} \] Where:
- \( n \) is the sample size
- \( s^2 \) is the sample variance
- \( \sigma^2 \) is the population variance
Given that:
- \( s^2 = 15.4 \)
- \( \sigma^2 = 14.8 \)
- Degrees of freedom \( df = 10 \) implies \( n-1 = 10 \), hence \( n = 11 \)
Now calculate the Chi-square value: \[ \chi^2 = \frac{(11-1) \times 15.4}{14.8} = \frac{10 \times 15.4}{14.8} = \frac{154}{14.8} \approx 10.41 \] Final Answer: \[ \boxed{10.41} \]