The table below displays data on the composition and perform

The table below displays data on the composition and performance of the Massachusetts Bubble Growth (MBG) technology stock fund over the last year. The table includes data on the distribution of stocks in the fund by technology sector (information technology (IT) or biotechnology) and by last year\'s \"performance\" (positive or negative net change in share price over the last year).

Regarding the stocks that made up the MBG fund last year, which of the following statements is true?

E) Technology sector and performance are statistically independent.

F) The fact that a given stock\'s performance was positive tells us nothing about its sector.

G) The fact that a given stock is from the biotech sector tells us nothing about its performance.

H) None of the above.

Solution

We learned that

P(positive|biotech) = 0.23/(0.23 + 0.07) = 0.7667
P(positive|IT) = 0.17/(0.17 + 0.53) = 0.2429

Thus, E is not true. These probabilities are not equal, hence, performance is dependent on sector. OPTION E IS INCORRECT.

As performance is dependent on sector, performance tells us about the sector, and sector tells us about the performance.

Hence, options F and G are also incorrect.

THUS, IT IS H: NONE OF THE ABOVE. [ANSWER]