You want to determine whether gender has an impact on attitudes toward police. You conduct a survey with a random sample of 220 individuals over the age of 18 asking your participants about their attitudes about police (positive/negative). The results are presented in the table below. You set your alpha level at 0.01.
a. Identify the independent and dependent variables and indicate the level of measurement for each variable.
b. Compute the percentages for every cell.
c. State your null hypothesis and your alternative hypotheses.
d. Compute the degrees of freedom.
e. State your decision rule
f. Compute expected frequencies for each cell.
g. Compute chi square.
h.Interpret your findings.
$$\begin{array} { | l | r | r | r | }
\hline & { \text { Male } } & \text { Female } & \
\hline \text { Positive } & 42 & 77 & 93 \
\hline \text { Negative } & 57 & 44 & 127 \
\hline & 99 & 121 & 220 \
\hline
\end{array}$$

Question

You want to determine whether gender has an impact on attitudes toward police. You conduct a survey with a random sample of 220 individuals over the age of 18 asking your participants about their attitudes about police (positive/negative). The results are presented in the table below. You set your alpha level at 0.01.
a. Identify the independent and dependent variables and indicate the level of measurement for each variable.
b. Compute the percentages for every cell.
c. State your null hypothesis and your alternative hypotheses.
d. Compute the degrees of freedom.
e. State your decision rule
f. Compute expected frequencies for each cell.
g. Compute chi square.
h.Interpret your findings.
 $$\begin{array} { | l | r | r | r | } 
\hline & { \text { Male } } & \text { Female } & \
\hline \text { Positive } & 42 & 77 & 93 \
\hline \text { Negative } & 57 & 44 & 127 \
\hline & 99 & 121 & 220 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The Answer is a. IV = gender: male, female (nominal).
DV = attitudes toward police: positive, negative (nominal).
b.

\begin{array} { | l | r | r | r | } \hline & ext { Male } & ext { Female } & \\hline & \mathrm { A } & \mathrm { B } & \& 42 & 77 & 119 \ ext { Positive } & ( 42.42 \% ) & ( 63.64 \% ) & ( 54.09 \% ) \\hline & \mathrm { C } & \mathrm { D } & \& 57 & 44 & 101 \ ext { Negative } & ( 57.58 \% ) & ( 36.36 \% ) & ( 45.91 \% ) \\hline & 99 ( 100 \% ) & 121 ( 100 \% ) & ( 100 \% ) \\hline\end{array}

c. H₀: There is no relationship between one's gender and one's attitudes toward police.
H₁: There is a relationship between one's gender and one's attitudes toward police.
d. df = (c - 1)(r - 1) = (2 - 1)(2 - 1) = 1.
e. You reject the null hypothesis if x² is greater than 6.635.
f. E(A) = (99 × 119)/220 = 53.55
E(B) = (121 × 119)/220 = 65.45
E(C) = (99 × 101)/220 = 45.45
E(D) = (121 × 101)/220 = 55.55
g.

\chi ^ { 2 } = \Sigma \frac { ( O - E ) ^ { 2 } } { E } = 9.866

\begin{array}{|l|c|c|c|c|c|}\hline ext { Cell } & O & E & O-E & (O-E)^{2} & {\begin{array}{c}(O- \E)^{2} / E\end{array}} \\hline \mathrm{A} & 42 & 53.55 & -11.55 & 133.4025 & 2.491 \\hline \mathrm{B} & 77 & 65.45 & 11.55 & 133.4025 & 2.038 \\hline \mathrm{C} & 57 & 45.45 & 11.55 & 133.4025 & 2.935 \\hline \mathrm{D} & 44 & 55.55 & -11.55 & 133.4025 & 2.401 \\hline & & & & \sum & 9.866 \\hline \end{array}

h. You reject the null hypothesis (α = 0.01) because χ² (9.866) is greater than 6.635, meaning that there is a statistically significant relationship between one's gender and one's attitudes toward police (x²(1) = 9.866, p < 0.01). Whereas 42.42% of males hold positive attitudes toward police, 63.64% of females expressed positive attitudes toward police.

You Want to Determine Whether Gender Has an Impact on Attitudes