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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset Vaia Explanations$ Math

13th Edition · 888 pages

ISBN: 9780134506593

Chapter 4: Q34E (page 227)

Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded was whether or not the citizen invested in the stock market. The accompanying table gives the number of Finnish citizens in each IQ score/investment category. Which group of Finnish citizens (market investors or noninvestors) has the highest average IQ score?
IQ Score
Invest in market
No investment
Totals
1
893
4659
5552
2
1340
9409
10749
3
2009
9993
12002
4
5358
19682
25040
5
8484
24640
33124
6
10270
21673
31943
7
6698
11260
17958
8
5135
7010
12145
9
4464
5067
9531
Totals
44651
113393
158044

Short Answer

Expert verified

The highest average IQ score is 28.46 for IQ score 1.

Step by step solution

01

Given information

The table shows the citizens in each IQ score or investment category. Here, it is also recorded that the citizen are invested in the stock market.

02

Calculating highest average IQ score

IQ Score	Invest in market	No investment	Totals	Average
1	893	4659	5552	28.46
2	1340	9409	10749	14.7
3	2009	9993	12002	13.16
4	5358	19682	25040	6.31
5	8484	24640	33124	4.77
6	10270	21763	31943	4.94
7	6698	11260	17958	8.8

8	5135	7010	12145	13.01
9	4464	5067	9531	16.58

Thus, the highest average IQ is 28.46 for IQ score 1.

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Most popular questions from this chapter

Find a $z$ -score, call it $z_{0}$ , such that

a. $P (z \leq z_{0}) = . 5080$

b. $P (z \geq z_{0}) = . 5517$

c. $P (z \geq z_{0}) = . 1492$

d. $P (z_{0} \leq z \leq . 59) = . 4773$

Assume that xhas an exponential distribution with $θ = 3$ .

Find

a. $P (x \leq 1)$

b. $P (x > 1)$

c. $P (x = 1)$

d. $P (x \leq 6)$

e. $P (2 \leq x \leq 10)$

Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of whether you are more likely to choose a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a shopping basket) than when your arm is extended (as when pushing a shopping cart), Exercise 2.85 (p. 112). The study measured choice scores (on a scale of 0 to 100, where higher scores indicate a greater preference for vice options) for consumers shopping under each of the two conditions. Recall that the average choice score for consumers with a flexed arm was 59, while the average for consumers with an extended arm was 43. For both conditions, assume that the standard deviation of the choice scores is 5. Also, assume that both distributions are approximately normally distributed.

a. In the flexed arm condition, what is the probability that a consumer has a choice score of 60 or greater?

b. In the extended arm condition, what is the probability that a consumer has a choice score of 60 or greater?

Mailrooms contaminated with anthrax. During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling mailrooms for the presence of anthrax spores. Let x equal the number of mailrooms contaminated with anthrax spores in a random sample of n mailrooms selected from a population of N mailrooms. The researchers showed that the probability distribution for x is given by the formula $P (x) = \frac{(\begin{matrix} k \\ x \end{matrix}) (\begin{matrix} N - k \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})}$

where k is the number of contaminated mailrooms in the population. (In Section 4.4 we identify this probability distribution as the hypergeometric distribution.) Suppose N = 100, n = 3, and k = 20.

a. Find p(0).

b. Find p(1)

. c. Find p(2).

d. Find p(3)

Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables?

a. The closing price of a particular stock on the New York Stock Exchange.

b. The number of shares of a particular stock that are traded each business day.

c. The quarterly earnings of a particular firm.

d. The percentage change in earnings between last year and this year for a particular firm.

e. The number of new products introduced per year by a firm.

f. The time until a pharmaceutical company gains approval from the U.S. Food and Drug Administration to market a new drug.

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