A survey investigated the public’s attitude toward the federal deficit. Each sam

Question

A survey investigated the public’s attitude toward the federal deficit. Each sampled citizen
was classified as to whether he or she felt the government should reduce the deficit or increase
the deficit, or if the individual had no opinion. The sample results of the study by
gender are reported below.
Reduce the Increase the No
Gender Deficit Deficit Opinion
Female 244 194 68
Male 305 114 25
Number of HDTVs Number of Households
0 7
1 27
2 28
3 18
4 10
5 or more 10
Total 100
At the .05 significance level, is it reasonable to conclude that gender is independent of a
person’s position on the deficit?

Explanation / Answer

Ans:1)

Ho:Gender is independent of a person's position on the deficit.
Ha:Gender is dependent of a person's position on the deficit.

Expected count=row sum*column sum/total sum

Degree of freedom=(2-1)*(3-1)=2

p-value=0

Significance level=0.05

As,p-value<0.05,We reject null hypothesis.

Hence,We do not have sufficient evidence to conclude that gender is independent of a
person’s position on the deficit.

2)

Chi square score=25.16

Degree of freedom=6-1=5

p-value=0.00013

As,p-value<0.05,We reject null hypothesis.

Observed(O) reduce deficit increase deficit No opinion Total Female 244 194 68 506 male 305 114 25 444 Total 549 308 93 950 Expected(E) reduce deficit increase deficit No opinion Total Female 292.41 164.05 49.53 506 male 256.59 143.95 43.47 444 Total 549 308 93 950 Chi- square=(O-E)2/E 8.02 5.47 6.88 9.14 6.23 7.84 Chi square score=8.02+5.47+6.88+9.14+6.23+7.84= 43.58

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