Violence and lack of discipline have become major problems in schools in the Uni
ID: 3235306 • Letter: V
Question
Violence and lack of discipline have become major problems in schools in the United States. A random sample of 300 adults was selected, and they were asked if they favor giving more freedom to school teachers to 1 punish students for violence and lack of discipline. The two-way classification of the responses of these adults is presented in the following table. In Favor (F) Against (A) No Opinion (N) Men (M) 93 70 12 Women (W) 87 32 6
a. Calculate the expected frequencies for this table assuming that the two attributes, gender and opinions on the issue, are independent.
b. Does the sample provide suficient information to conclude that the two attributes, gender and opinions of adults, are dependent? Use a 1% significance level.
Explanation / Answer
a. First the observed table .
Expected Table
i am doing it for one value , rest can be calculated with same pattern.
e.g. expected frequency for IN favour and Men is = (175 * 180 )/300 = 105
so Now first we describes hypothesis.
Null Hypothesis : H0: Opinion regarding punishment for children is independent of gender.
Alternative Hypothesis : Ha : Opinion regarding punishment for children is based on gender.
So chi - square statistics table for each respective value for (Oi- Ei)2 /Ei
The chi - square statistic X2 = 8.253
Critical value for alpha = 0.01 and dF = (2-1 * (3-1) = 2
X2critical = 9.210
X2 < X2critical so we cannot reject the null hypothesis and can conclude that opinions are independent of genders.
Men(m) Women(W) Total In Favour(F) 93 87 180 Against(A) 70 32 102 No Optinion (N) 12 6 18 Total 175 125 300Related Questions
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