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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