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

question 8

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 $z$ 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 $n = 104$ and $\alpha = 0.10$ .

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

Recognize inferential statistics and their purpose in drawing conclusions from sample data.

Understand the concepts and implications of Type I and Type II errors in hypothesis testing.

Grasp the fundamental statistical distributions and their relevance to different types of data.

Appreciate the role of sample size in statistical confidence and error minimization.

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Definitions:

Oxidized

A chemical change in which a substance loses electrons, often associated with the addition of oxygen or the loss of hydrogen.

Chemical Reaction

A process that leads to the transformation of one set of chemical substances to another through the making and breaking of bonds between atoms.

Rust

A type of fungal disease that affects plants, causing reddish-brown spots, or the oxidation of iron and its alloys resulting in reddish-brown flaking coatings.

Iron

A chemical element with symbol Fe, important in biological processes and industrial applications.