An investment company is looking to hire one of three different stockbrokers (J, K, and L). In order to measure their ability to predict the future value of stocks, each stockbroker will be given historical data on a set of stocks and then asked to predict whether each stock increased or decreased in value within a certain time period. The investment company has access to a large database of historical stock performance data. A random sample of 500 stocks that were known to have increased in value during the time period is selected. Each stock was then randomly assigned to one of the three stockbrokers. The table shows the number of stocks correctly predicted to increase in value and incorrectly predicted to decrease in value for each stockbroker.

(a) Compare the relative frequencies of stocks correctly predicted to increase in value for each stockbroker to determine which is highest.

The investment company selected a second random sample of 300 stocks that were known to have decreased in value during the time period. Each stock was then randomly assigned to one of the three stockbrokers. The segmented bar graph shows the distribution of the number of stocks correctly predicted to decrease in value and incorrectly predicted to increase in value for each stockbroker.

(b) Write a few sentences describing what the graph reveals about the association between stockbroker and prediction accuracy among the 300 stocks that decreased in value.
(c) For each stockbroker, give a statistical reason why the investment company might choose to hire the stockbroker to make predictions about the future value of stocks. Do not perform an inferential procedure.

The investment company plans to use the sample data to investigate whether there is convincing statistical evidence, at α=0.10, that the proportion of stocks that would be correctly predicted to increase in value by Stockbroker J is greater than the proportion of stocks that would be correctly predicted to decrease in value by Stockbroker J.

(d) Name the appropriate test and state, in words, the hypotheses.
(e) State the conditions for the appropriate test, and explain why the conditions are met.
(f) The test statistic for the appropriate test is 1.375 (increased minus decreased). Based on the result of the hypothesis test, what conclusion should the investment company make? Justify your answer.