Math  /  Data & Statistics

QuestionIn Bloomington, they randomly sampled 210 female voters, and 440 male voters. They collected data on the respondent's opinion on an environmental bond issue. We want to know whether there is good evidence that one's gender influences whether a person is for or against the bond issue. Use α=0.1\alpha=0.1. \begin{tabular}{|c|c|c|c|} \hline & For Bond Issue & Against Bond Issue & Total \\ \hline Men & 51 & 159 & 210 \\ \hline Women & 39 & 401 & 440 \\ \hline Total & 90 & 560 & 650 \\ \hline \end{tabular} a) What is the correct null hypothesis? Ho:p1p2p3p4H_{o}: p_{1} \neq p_{2} \neq p_{3} \neq p_{4} Ho:p1=p2=p3=p4H_{o}: p_{1}=p_{2}=p_{3}=p_{4} HoH_{o} : Gender and Bond Issue Attitudes are dependent. HoH_{o} : Gender and Bond Issue Attitudes are Independent. b) Fill in the expected values, round answers to 1 decimal place. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Expected \\ Values \end{tabular} & For Bond Issue & \begin{tabular}{c} Against \\ Bond Issue \end{tabular} \\ \hline Men & & \\ \hline Women & & \\ \hline \end{tabular} c) Chi Square Test Statistic == \square Round answer to 1 decimal place.
Degree's of Freedom == \square d) The pp-value == \square Round answer to 3 decimal places.

Studdy Solution
Calculate the p-value using the chi-square distribution table or calculator for χ2=29.3\chi^2 = 29.3 and 1 degree of freedom.
The p-value is approximately:
p=0.000 p = 0.000
The solution is:
a) Null Hypothesis: H0:Gender and Bond Issue Attitudes are Independent. H_0: \text{Gender and Bond Issue Attitudes are Independent.}
b) Expected Values:
Expected ValuesFor Bond IssueAgainst Bond IssueMen29.1180.9Women60.9379.1\begin{array}{|c|c|c|} \hline \text{Expected Values} & \text{For Bond Issue} & \text{Against Bond Issue} \\ \hline \text{Men} & 29.1 & 180.9 \\ \hline \text{Women} & 60.9 & 379.1 \\ \hline \end{array}
c) Chi Square Test Statistic =29.3 = 29.3
Degrees of Freedom =1 = 1
d) The p p -value =0.000 = 0.000

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