Solve the Problem $\chi ^ { 2 }$ Values Can Be Approximated as Follows

question 83

Multiple Choice

Solve the problem.
-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 $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z }$ is the critical value. To find the lower critical value, the negat 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 $\mathrm { n } = 144$ and $\alpha = 0.10$ .

• A) \(\chi ^ { 2 } \approx 116.985\) and \(\chi ^ { 2 } \approx 172.721\)
• B) \(\chi ^ { 2 } \approx 116.082\) and \(\chi ^ { 2 } \approx 171.624\)
• C) \(\chi ^ { 2 } \approx 122.635\) and \(\chi ^ { 2 } \approx 166.004\)
• D) \(\chi ^ { 2 } \approx 121.710\) and \(\chi ^ { 2 } \approx 164.928\)

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Definitions:

Balance of Payments

A financial statement summarizing a country's transactions with the rest of the world over a specified period, including trade, investment, and financial transfers.

Depreciation

The process of allocating the cost of a tangible asset over its useful life, reflecting wear and tear or obsolescence.

Balance Of Trade

The difference between a country's exports and imports of goods, without including services.

Goods Exports

Refers to the selling and shipment of tangible products from one country to another, contributing to a nation’s gross domestic exports.