The Long and the Short of it We all hate the idea of irrational discrimination a

Question

The Long and the Short of it We all hate the idea of irrational discrimination against others, whether it's based on race, sex, religion, or whatever. But are we actually aware of our own prejudices? Studies suggest that there is a particular group of people who have a distinct advantage over others, in fields as diverse as politics, business, and finding a partner. Are they super-intelligent, super-charismatic, or endowed with amazing personal qualities...? Nope, they're just tall. Here's an example of some of the evidence. The Fortune 500 list is a list of the 500 richest business in the US. In 2005, a study was done of the CEOs (heads) of 250 of the businesses on this list, all of whom were male. It was found that 58% of the CEOs were over 6 feet tall (183cm).^4 In the US population, 14.5% of adult men are over 6 feet tall. (a) Decide on an appropriate method to test whether these figures give evidence that there are more tall men among the company heads than would be expected by chance. Apply the method to reach your conclusion, showing all the formulation and working that you usually show when you use this method. (b) You should have found that the answer for (a) was highly significant. Does this prove that tall people have an advantage in business, just because of their height? Is there any other possible explanation for the result? See if you can think of a different explanation for there being a surplus of tall people in the CEO sample that is not connected with height-based discrimination. Do you find your alternative explanation more or less convincing than the explanation of height-based discrimination?

Explanation / Answer

(a) Here, we have to find that if there are more tall men among the company heads than it would be normally (by chance)

So, we can apply hypothesis test for one sample proportion.

Here sample size = 250

Proportion of CEOs who has height more than 6 feet p^= 58% = 0.58

Proportion of people who has height more than 6 feet in US p0= 14.5% = 0.145

so here,

Null Hypothesis : Ho : Proportion of CEOs who has more height than 6 ft is same as that would be expected by chance. p = p0

Alternative Hypothesis : Ha : Proportion of CEOs who has more height than 6 ft is more than what would be expected by chance. p > p0

so Test statistic

Z = (p - p0 )/ sqrt [p0 (1 -p0)/N]

Z = (0.58 - 0.145)/ sqrt [0.145 * 0.855/250]

Z = 0.435/0.02227 = 19.5

so here we can that Z > Zcrticial , so we can reject the null hypothesis and can conclude that Proportion of CEOs who has more height than 6 ft is more than what would be expected by chance.

(b) Yes, the answer found is highly significant. But, that doesn't prove that more height make people successful in business. Correlation doesn't imply causation. Tall people doesn't have any advantage in business, just because of their height. Instead of height, there are some other factors like confidence and good communication skills or management skills are the features which prompts the success at higher level. A height above 6 ft. may inculcate a strong confidence in the person that increases the chances of more success in business.

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