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Stock market participation and IQ.Refer to The Journal of Finance(December 2011) study of whether the decisionto invest in the stock market is dependent on IQ, Exercise3.46 (p. 182). The summary table giving the number ofthe 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.

IQ Score

Invest in Market

No Investment

Totals

1

2

3

4

5

6

7

8

9

893

1,340

2,009

5,358

8,484

10,270

6,698

5,135

4,464

4,659

9,409

9,993

19,682

24,640

21,673

11,260

7,010

5,067

5,552

10,749

12,002

25,040

33,124

31,943

17,958

12,145

9,531

Totals

44,651

113,393

158,044

Source:Based on M. Grinblatt, M. Keloharju, and J. Linnainaa, 鈥淚Q and Stock Market Participation,鈥 The Journal of Finance, Vol. 66, No. 6, December 2011 (data from Table 1 and Figure 1).

a.Given that the Finnish citizen has an IQ score of 6 or higher, what is the probability that he/she invests in the stock market?

b.Given that the Finnish citizen has an IQ score of 5 or lower, what is the probability that he/she invests in the stock market?

c.Based on the results, parts a and b, does it appear that investing in the stock market is dependent on IQ? Explain.

Short Answer

Expert verified
  1. 37%
  2. 20.91%
  3. Yes

Step by step solution

01

 Step 1: Finding the probability that a Finnish citizen with an IQ above 6 will invest in the stock market

As we only want the probability for citizens with IQ scores of 6 and above, we will first add the number of citizens in all 3 columns with an IQ of 6 and above.

Invest in Market = 10,270+ 6698 + 5135 + 4464 = 26,567

No investment = 21673 + 11260 + 7010 + 5067 = 45,010

Total = 26567 + 45010 = 71,577

Let A be the total number of people with an IQ of 6 or above.

B be the number of people with an IQ of 6 or above who invest in the market.

To find the probability that the Finnish citizen has an IQ score of 6 or higher and invests in the stock market,

P=BA=2656771577=0.37=37%

Therefore,P(B|A)=37%.

02

Computing the probability that a Finnish citizen with an IQ of 5 or less invests in the market

Let鈥檚 add the number of citizens with an IQ of 5 or less for all columns,

Invest in Market = 893 + 1340 + 2009 + 5358 + 8484 = 18,084

No investment = 4659 + 9409 + 9993 + 19682 + 24640 = 68,383

Total = 18084 + 68383 = 86,467

Let鈥檚 assume

C = total number of people with an IQ of 5 or below

D = number of people with an IQ of 5 or below who invest in the market

P=DC=1808486467=0.2091=20.91%

Therefore,P(C|D)=20.91%

03

Explaining whether investing in stocks depends on IQ

P(B|A)>P(C|D)

Investing in stocks does depend on IQbecause the probability that a citizen with IQ of 6 or above is greater than the probability of a citizen investing who has IQ of 5 or below.

There are more chances that a person with a higher than 6 IQ will invest in stocks.

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