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Solve the Problem χ2\chi ^ { 2 } Values Can Be Approximated as Follows

question 16

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Solve the problem. For large numbers of degrees of freedom, the critical χ2\chi ^ { 2 } values can be approximated as follows: x2=12(z+2k1) 2x ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 } , where k\mathrm { k } is the number of degrees of freedom and zz is the critical value. To find the lower critical value, the negative zz -value is used, to find the upper critical value, the positive zz -value is used. Use this approximation to estimate the critical value of χ2\chi ^ { 2 } in a two-tailed hypothesis test with n=104n = 104 and α=0.10\alpha = 0.10 .

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Definitions:

Self-Kindness

Being kind to yourself.

Self-Efficacy

An individual's belief in their capacity to execute behaviors necessary to produce specific performance attainments.

Self-Concept

An individual's comprehensive understanding of themselves, encompassing beliefs, attitudes, and perceptions about one’s abilities, appearance, and personality.

Self-Enhancement

The psychological process of improving one's image by gaining positive feedback from the external environment and adopting a favorable interpretation of oneself.

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