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 problem: You need to find the chi-square value \( \chi^2 \) such that the cumulative probability to the left of this value is 0.010, i.e., \( P(X^2 < \chi^2) = 0.010 \), with degrees of freedom \( df = 50 \).
2. Understand that chi-square tables typically provide the right-tail probabilities \( P(X^2 > \chi^2) \). Since you want the left-tail probability, convert it to the right-tail probability using the complement rule: \( P(X^2 > \chi^2) = 1 - 0.010 = 0.990 \).
3. Locate the row in the chi-square table corresponding to \( df = 50 \). Then, find the chi-square value that corresponds to a right-tail probability of 0.990 (which matches the left-tail probability of 0.010).
4. Read off or interpolate the chi-square value from the table for \( df = 50 \) and right-tail probability 0.990. This value is the \( \chi^2 \) such that \( P(X^2 < \chi^2) = 0.010 \).
5. Verify your answer by checking that the cumulative probability to the left of the found \( \chi^2 \) value is indeed 0.010, either by using the table or a chi-square distribution calculator.