Question

In: Statistics and Probability

QUESTION 1: For reasons known only to social scientists, the General Social Survey (GSS) regularly asks...

QUESTION 1:

For reasons known only to social scientists, the General Social Survey (GSS) regularly asks its subjects their astrological sign. Here are the counts of responses for the 2012 GSS:

Sign Aries Taurus Gemini Cancer Leo Virgo
Count 142 155 160 156 187 169
Sign Libra Scorpio Sagittarius Capricorn Aquarius Pisces
Count 188 152 155 142 166 150

If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are they? Use α=0.05α=0.05.

χ2(±0.0001)=χ2(±0.0001)=

P(±0.0001)=P(±0.0001)=

There is no evidence that all 12 signs are not equally likely.

There is evidence that all 12 signs are not equally likely.

QUESTION 2:

We suspect that people who rely entirely on cell phones will as a group be younger than those who have a landline telephone. Do data confirm this guess? The Pew Research Center interviewed separate random samples of cell-only and landline telephone users and broke down the samples by age group

LANDLINE SAMPLE CELL-ONLY SAMPLE
Age 18-29 372 337
Age 30-49 337 1251
Age 50-64 141 1627
Age 65 or older 30 1473
Total 880 4688

(a) Should you use a chi-square test of independence or homogeneity:

homogeneity

independence

(b) Carry out a chi-square test. Test H0:H0: the distribution of age groups is the same for landline and cell-only individuals versus Ha:Ha: the distributions are different. Use α=0.01α=0.01.

χ2(±0.0001)=χ2(±0.0001)=

P(±0.0001)=P(±0.0001)=

There is no evidence of an association between age group and the type of telephone
There is evidence of an association between age group and the type of telephone

Solutions

Expert Solution

Categories Observed Expected (fo-fe)2/fe
Aries 142 1922*0.08333=160.16 (142-160.16)2/160.16 = 2.059
Taurus 155 1922*0.08333=160.16 (155-160.16)2/160.16 = 0.166
Gemini 160 1922*0.08333=160.16 (160-160.16)2/160.16 = 0
Cancer 156 1922*0.08333=160.16 (156-160.16)2/160.16 = 0.108
Leo 187 1922*0.08333=160.16 (187-160.16)2/160.16 = 4.498
Virgo 169 1922*0.08333=160.16 (169-160.16)2/160.16 = 0.488
Libra 188 1922*0.08333=160.16 (188-160.16)2/160.16 = 4.839
Scorpio 152 1922*0.08333=160.16 (152-160.16)2/160.16 = 0.416
Sagittarius 155 1922*0.08333=160.16 (155-160.16)2/160.16 = 0.166
Capricorn 142 1922*0.08333=160.16 (142-160.16)2/160.16 = 2.059
Aquarius 166 1922*0.08333=160.16 (166-160.16)2/160.16 = 0.213
Pisces 150 1922*0.08333=160.16 (150-160.16)2/160.16 = 0.645
Sum = 1922 1922 15.657

orchestra answered 1 year ago
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