Use a table to find or estimate ${\chi }^2$ such that:
(Area to the left)
$df=50$

• A. 27.99
• B. 29.71
• C. 76.15
• D. 79.49

Answer: (B)

Verified step by step guidance

1. Identify the distribution and parameters: We are dealing with a chi-square distribution with degrees of freedom (df) equal to 50.
2. Understand the probability statement: We want to find the chi-square value \( \chi^2 \) such that the probability that the chi-square random variable \( X^2 \) is less than this value is 0.010, i.e., \( P(X^2 < \chi^2) = 0.010 \). This means the area to the left of \( \chi^2 \) is 0.010.
3. Use the chi-square distribution table: Since most chi-square tables provide critical values for the right-tail probabilities (e.g., \( P(X^2 > \chi^2) = \alpha \)), convert the left-tail probability to a right-tail probability by calculating \( 1 - 0.010 = 0.990 \). So, we look for the chi-square value where \( P(X^2 > \chi^2) = 0.990 \).
4. Locate the value in the table: Find the row corresponding to df = 50 and the column corresponding to the right-tail probability of 0.990. The value at this intersection is the chi-square value \( \chi^2 \) such that \( P(X^2 < \chi^2) = 0.010 \).
5. Interpret the result: The chi-square value found from the table is the estimate for \( \chi^2 \) that satisfies the given probability condition.