A state is considering legislation to establisha law

meiprate81w

meiprate81w

Answered question

2022-03-18

A state is considering legislation to establisha law to help homeless individuals. A sample of 309 individuals regarding their opinions on the potential new law. Is there a relationship between sex and support for this law? Calculate the expected frequencies and compute a chi-square test for a statistically significant relationship between sex and support for the new law. Be sure to round to the second decimal.
 Sex  Support  Male  Female  For 98101 Against 2981 

Answer & Explanation

Talan Kent

Talan Kent

Beginner2022-03-19Added 4 answers

The given information is about the sample of 309 individuals regarding their opinions on the potential new law.
Hypotheses:
H0: There is no significant relationship between sex and support for the new law.
H1: There is a significant relationship between sex and support for the new law.
Observed Frequencies:
 Sex  Support  Male  Female  Total  For 98101199 Against 2981110 Total 127182309 
Calculate the expected frequencies:
 Sex  Support  Male  Female  Total  For 127×199309=81.790182×199309=117.210199 Against 127×110309=45.210182×110309=64.790110 Total 127182309 
Chi-square test statistic:
χ2={i=1}n(OiEi)2Ei
Calculate the chi-square test statistic value is as follows:
χ2=(9881.79)281.79+(101117.21)2117.21+(2945.21)245.21+(8164.79)264.79
=3.2127+2.2418+5.8121+4.0556
=15.3222
15.32
Therefore, the value of chi-square test statistic is 15.32.
P-value:
Degrees of freedom:
(r – 1)(c – 1) = (2 – 1)(2 – 1) = 1.
Therefore, the degrees of freedom is 1.
Calculate the p-value using Excel is as follows:
Therefore, the p-value is 0.0001.
Decision rule:
Let assume level of significance is 0.05.
If p-value < level if significance, then reject the null hypothesis.
Here, p-value (0.0001) < level of significance (0.05), then reject the null hypothesis.
Conclusion:
Therefore, there is an evidence to conclude that there is a significant relationship between sex and support for the new law.

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