Chapter 11.1, Problem 10E

To determine

To perform chi-square goodness of fit test.

Answer to Problem 10E

There is not sufficient evidence to support the claim that the all 12 signs are not equally likely.

Explanation of Solution

Given:

Sign	Count	Frequency
Aries	321	0.0833
Tarus	360	0.0833
Gemini	367	0.0833
Cancer	374	0.0833
Leo	383	0.0833
Virgo	402	0.0833
Libra	392	0.0833
Scorpio	329	0.0833
Sagittarius	331	0.0833
Capricorn	354	0.0833
Aquarius	376	0.0833
Pisces	355	0.0833
Total	4344	1.0000

Calculation:

The null and alternative hypotheses:

  $H_0:p_1=p_2=\mathrm{...}=p_{12}=\frac{1}{12}=0.0833$

  $H_a:Atleastoneofthe{p}_i’sisincorrect.$

Using excel,

Sign	observed	expected	O - E	(O - E)² / E	% of chisq
Aries	321	362.000	-41.000	4.644	23.50
Tarus	360	362.000	-2.000	0.011	0.06
Gemini	367	362.000	5.000	0.069	0.35
Cancer	374	362.000	12.000	0.398	2.01
Leo	383	362.000	21.000	1.218	6.16
Virgo	402	362.000	40.000	4.420	22.37
Libra	392	362.000	30.000	2.486	12.58
Scorpio	329	362.000	-33.000	3.008	15.22
Sagittarius	331	362.000	-31.000	2.655	13.43
Capricorn	354	362.000	-8.000	0.177	0.89
Aquarius	376	362.000	14.000	0.541	2.74
Pisces	355	362.000	-7.000	0.135	0.68
Total	4344	4344.000	0.000	19.762	100.00
	19.76	chi-square
	11	Df
	.0487	p-value

Chi-square test statistic = 19.76

The p-value = 0.0487

Decision: The p-value > 0.01, fail to reject H0.

Conclusion: There is not sufficient evidence to support the claim that the all 12 signs are not equally likely.