Find the Critical Value or Values Of $\chi ^ { 2 }$

question 18

Multiple Choice

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows:
$$\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$$ where $k$ is the number of degrees of freedom and $z$ is the critical value. To find the lower critical value, the negative $z$ -value is used, to find the upper critical value, the positive $z$ -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a two-tailed hypothesis test with $\mathrm { n } = 104$ and $\alpha = 0.10$ .

• A) \(\chi ^ { 2 } \approx 84.992\) and \(\chi ^ { 2 } \approx 121.646\)
• B) \(\chi ^ { 2 } \approx 80.300\) and \(\chi ^ { 2 } \approx 127.406\)
• C) \(\chi ^ { 2 } \approx 81.186\) and \(\chi ^ { 2 } \approx 128.520\)
• D) \(\chi ^ { 2 } \approx 85.903\) and \(\chi ^ { 2 } \approx 122.735\)

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Definitions:

Fixed Cost

Expenses that remain constant for a company regardless of its level of production or sales volume, such as leases and managerial salaries.

Salvage Company

A firm that specializes in recovering and processing materials from failed projects or discarded products.

Net Working Capital

The disparity between a company's immediate assets and immediate liabilities, showcasing its short-term economic well-being.

Straight-Line Depreciation

An accounting method that allocates the cost of a tangible asset evenly over its useful life.