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

question 57

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) \(\chi ^ { 2 } \approx 84.992\) and \(\chi ^ { 2 } \approx 121.646\)
• 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) \(\chi ^ { 2 } \approx 85.903\) and \(\chi ^ { 2 } \approx 122.735\)

---

Definitions:

Semiannual Interest

Interest that is calculated and paid twice a year.

Bond Premium

When a bond's selling price surpasses its original issued cost, known as its face value.

Annual Interest

The amount of interest charged or earned over a year on borrowed capital or investment principal.

Present Value

The contemporary financial worth of a future sum or ongoing cash flows, evaluated at a designated rate of return.