Question

In: Math

A company manager believes that a person’s ability to be a leader is directly correlated to...

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.

___

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

___

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

Yes/No

Solutions

Expert Solution

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.

milcah answered 1 year ago
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