Find the type and the number of variables for which the Chi-square goodness-of-fir tests are used.

$\overline{\begin{array}{cc}& \text{Afraid to walk at night?}\\ & \text{Yes}& \text{No}& \text{Total}\\ \text{Male}& 173& 598& 771\\ \text{Female}& 393& 540& 933\\ \text{Total}& 566& 1138& 1704\\ \text{Source:}2014GSS\end{array}}$
If the chi-square $(\chi 2)$ test statistic $=73.7$ what is the p-value you would report? Use Table C.Remember to calculate the df first.
Group of answer choices
$P>0.250$
$P=0.01$
$P<0.001$
$P<0.002$

$\begin{array}{|cc|}\hline & \text{Right-Tail Probability}\\ df& 0.250& 0.100& 0.050& 0.025& 0.010& 0.005& 0.001\\ 1& 1.32& 2.71& 3.84& 5.02& 6.63& 7.88& 10.83\\ 2& 2.77& 4.61& 5.99& 7.38& 9.21& 10.60& 13.82\\ 3& 4.11& 6.25& 7.81& 9.35& 11.34& 12.84& 16.27\\ 4& 5.39& 7.78& 9.49& 11.14& 13.28& 14.86& 18.47\\ 5& 6.63& 9.24& 11.07& 12.83& 15.09& 16.75& 20.52\\ 6& 7.84& 10.64& 12.59& 14.45& 16.81& 18.55& 22.46\\ 7& 9.04& 12.02& 14.07& 16.01& 18.48& 20.28& 24.32\\ 8& 10.22& 13.36& 15.51& 17.53& 20.09& 21.96& 26.12\\ 9& 11.39& 14.68& 16.92& 19.02& 21.67& 23.59& 27.88\\ 10& 12.55& 15.99& 18.31& 20.48& 23.21& 25.19& 29.59\\ 11& 13.70& 17.28& 19.68& 21.92& 24.72& 26.76& 31.26\\ 12& 14.85& 18.55& 21.03& 23.34& 26.22& 28.30& 32.91\\ 13& 15.98& 19.81& 22.36& 24.74& 27.69& 29.82& 34.53\\ 14& 17.12& 21.06& 23.68& 26.12& 29.14& 31.32& 36.12\\ 15& 18.25& 22.31& 25.00& 27.49& 30.58& 32.80& 37.70\\ 16& 19.37& 32.54& 26.30& 28.85& 32.00& 34.27& 39.25\\ 17& 20.49& 24.77& 27.59& 30.19& 33.41& 35.72& 40.79\\ 18& 21.60& 25.99& 28.87& 31.53& 34.81& 37.16& 42.31\\ 19& 22.72& 27.20& 30.14& 32.85& 36.19& 38.58& 43.82\\ 20& 23.83& 28.41& 31.41& 34.17& 37.57& 40.00& 45.32\\ \hline\end{array}$

A chi-square value of 6.15 is calculated from data in a $4x5$ contingency table. Assuming $\alpha =0.05$, identify the critical value.
26.217
31.410
21.026
16.919

$\begin{array}{cc}& \text{Children at home?}\\ \text{Observed}& \begin{array}{|cccc|}\hline \text{ College Major }& \text{ Yes }& \text{ No }& \text{ Totals }\\ \text{ Applied Behavioral Science }& 30& 10& 40\\ \text{ Criminal Justice }& 10& 7& 17\\ \text{ Political Science }& 10& 10& 20\\ \text{ Psychology }& 32& 11& 43\\ \text{ Totals }& 82& 38& 129\\ {\chi }^2=5.37& & & \\ \hline\end{array}\end{array}$
1. How many variables are involved in this chi-square test?
2. Which type of chi-square test is this? Goodness of Fit or Test of Independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table, is the result of this test statistically significant? Yes or No