Question

A company manager believes that a person’s ability to be a leader is directly correlated to their zodiac sign. He never selects someone to chair a committee without first evaluating their zodiac sign. An irate employee sets out to prove her manager wrong. She claims that if zodiac sign truly makes a difference in leadership, then a random sample of 200 CEO’s in our country would reveal a difference in zodiac sign distribution. She finds the following zodiac signs for her random sample of 200 CEO’s:

Births	Signs
23	Aries
12	Taurus
16	Gemini
20	Cancer
14	Leo
16	Virgo
15	Libra
14	Scorpio
20	Sagittarius
11	Capricorn
17	Aquarius
22	Pisces

Can she conclude that zodiac sign makes a difference in whether or not a person makes a good leader?

Hypotheses:

H₀: There is a difference/no difference in leadership ability based on zodiac sign.

H₁: There is a difference/no difference in leadership ability based on zodiac sign.

Enter the test statistic - round to 4 decimal places.

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Enter the p-value - round to 4 decimal places.

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Can it be concluded that there is a statistically significant difference in leadership ability based on zodiac sign?

Yes/No

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Aries	23	0.083333	200 * 0.083333 = 16.6666	(23 - 16.6666)²/16.6666 = 2.4067
Taurus	12	0.083333	200 * 0.083333 = 16.6666	(12 - 16.6666)²/16.6666 = 1.3066
Gemini	16	0.083333	200 * 0.083333 = 16.6666	(16 - 16.6666)²/16.6666 = 0.0267
Cancer	20	0.083333	200 * 0.083333 = 16.6666	(20 - 16.6666)²/16.6666 = 0.6667
Leo	14	0.083333	200 * 0.083333 = 16.6666	(14 - 16.6666)²/16.6666 = 0.4266
Virgo	16	0.083333	200 * 0.083333 = 16.6666	(16 - 16.6666)²/16.6666 = 0.0267
Libra	15	0.083333	200 * 0.083333 = 16.6666	(15 - 16.6666)²/16.6666 = 0.1667
Scorpio	14	0.083333	200 * 0.083333 = 16.6666	(14 - 16.6666)²/16.6666 = 0.4266
Sagittarius	20	0.083333	200 * 0.083333 = 16.6666	(20 - 16.6666)²/16.6666 = 0.6667
Capricorn	11	0.083333	200 * 0.083333 = 16.6666	(11 - 16.6666)²/16.6666 = 1.9266
Aquarius	17	0.083333	200 * 0.083333 = 16.6666	(17 - 16.6666)²/16.6666 = 0.0067
Pisces	22	0.083333	200 * 0.083333 = 16.6666	(22 - 16.6666)²/16.6666 = 1.7067
Total	200	1.00	200	9.7600

Null and Alternative hypothesis:

H₀: There is a no difference in leadership ability based on zodiac sign.

H₁: There is a a difference in leadership ability based on zodiac sign.

Test statistic:

χ² = ∑ ((O-E)²/E) = 9.7600

df = n-1 = 11

p-value:

p-value = CHISQ.DIST.RT(9.76, 11) = 0.5521

Decision:

p-value > 0.05, Do not reject the null hypothesis

No, it cannot be concluded that there is a statistically significant difference in leadership ability based on zodiac sign.