On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows: Determine the expected frequencies for both the Democrats and Republicans who favor the tax cut proposal for the chi-square test of independence.
A)85,118
B)67.3,67.3
C)100.5,102.5
D)169.2,234.8

Question

On the most recent tax cut proposal,a random sample of Democrats and Republicans in the Congress cast their votes as follows:  Determine the expected frequencies for both the Democrats and Republicans who favor the tax cut proposal for the chi-square test of independence.
A)85,118 
B)67.3,67.3 
C)100.5,102.5 
D)169.2,234.8

Quizplus · Accepted Answer

To determine the expected frequencies, we first need to find the overall proportion of Democrats and Republicans who favored the tax cut proposal.

- Democrats: 22/(22+28) = 0.44
- Republicans: 63/(63+79) = 0.44

Next, we multiply these proportions by the total number of Democrats and Republicans in the sample:

- Expected number of Democrats who favor tax cut = 50 x 0.44 = 22
- Expected number of Republicans who favor tax cut = 142 x 0.44 = 62.48 (rounded to 62.5)

Therefore, the expected frequencies are:

- Democrats: 22
- Republicans: 62.5

Rounded to the nearest whole number, this becomes:

- Democrats: 22
- Republicans: 63

So the correct answer is C: 100.5, 102.5 (rounded to the nearest decimal).

On the Most Recent Tax Cut Proposal,a Random Sample of Democrats