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

question 31

Multiple Choice

Solve the problem. For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows: $x ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$ , where $\mathrm { k }$ 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 right-tailed hypothesis test with $n = 143$ and $\alpha = 0.01$ .

• A) \(X ^ { 2 } \approx 189.286\)
• B) \(\chi ^ { 2 } \approx 188.134\)
• C) \(x ^ { 2 } \approx 183.411\)
• D) \(\chi ^ { 2 } \approx 184.549\)

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Definitions:

Willingness to Pay

The maximum amount a consumer is ready to spend for a good or service.

Surplus

The situation where the quantity supplied of a product exceeds the quantity demanded at a given price.

Negative Externality

An economic situation where a third party is negatively affected by the actions of others, typically not reflected in the cost of those actions, such as pollution.

Common-Resource Problem

A dilemma in the management of resources that are available to all but are susceptible to overuse and depletion because they are not excludable.