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Chapter 8: Q8CQQ (page 356)

Chi-Square Test In a test of the claim that\(\sigma \)= 15 for the population of IQ scores of professional athletes, we find that the rightmost critical value is\(\chi _R^2\)= 40.646. Is the leftmost critical\(\chi _L^2\)value equal to -40.646?

Short Answer

Expert verified

No, the left most critical value \(\chi _L^2\) is not equal to -40.646.

Step by step solution

01

Given information

It is claimed that the population standard deviation of IQ scores is equal to 15.

The right most critical value \(\chi _R^2\) is equal to 40.646.

02

Critical Value of \({\chi ^2}\)

It is known that the chi-square distribution can assume values that are positive as chi-square is the sum of the square of the normal distribution.

A squared value can never be negative.

Thus, the critical value of the chi-square distribution can never be negative.

Therefore, the value of \(\chi _L^2\) cannot be equal to -40.646.

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