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Students are classified according to religious preference (Buddhist, Jewish, Protestant, Roman Catholic, or Other) and political affiliation (Democrat,...

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Basic Math

Students are classified according to religious preference(Buddhist, Jewish,

Protestant, Roman Catholic, or Other) and political affiliation(Democrat, Republican,

Independent, or Other).

RELIGIOUS PREFERENCE AND POLITICALAFFILIATION

RELIGIOUS PREFERENCE

POLITICAL

AFFILIATION BUDDHIST JEWISH PROTESTANT ROM. CATH. OTHERTOTAL

Democrat 30 30 40 60 40 200

Republican 10 10 40 20 20 100

Independent 10 10 20 20 40 100

Other 0 0 0 0 100 100

Total 50 50 100 100 200 500

(a) Is anything suspicious about these observedfrequencies?

(b) Using the .05 level of significance, testthe null hypothesis that these two variables

are independent.

(c) If appropriate, estimate the effectsize

Answer & Explanation Solved by verified expert
3.9 Ratings (438 Votes)

(a)

Some observed frequencies are zero which is suspicious.

(b)

Hypotheses are:

H0: The two variables Political affiliation and religious preference are independent.

Ha: The two variables Political affiliation and religious preference are not independent.

Following is the output of chi square test statistics

Chi-square Contingency Table Test for Independence
  
Buddhist   Jewish   Protestant   Rom. Cath.   Other    Total  
   Democrat    30 30 40 60 40 200
Republican    10 10 40 20 20 100
Independent    10 10 20 20 40 100
Other    0 0 0 0 100 100
Total    50 50 100 100 200 500
220.00 chi-square
12 df
2.37E-40 p-value
.663 Phi coefficient
.383 Cramér's V

The p-value of the test is;

p-value = 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.

That is we can not conclude that the two variables Political affiliation and religious preference are independent.

(c)

The effect size is: 0.663

It is large effect size.
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