Question

A young investor believes that he can beat the market by picking stocks that will increase in value. Assume that on average 46% of the stocks selected by a portfolio manager will increase over 12 months. Of the 27 stocks that the young investor bought over the last 12​ months, 15 have increased. Can he claim that he is better at predicting increases than the typical portfolio​ manager? Test at α=0.05

Question: Calculate the test statistic.

Answer: _______________________ (round to two decimal places as needed.)

Question: What is the P-Value for the test statistic ?

Answer: _______________________ (round to three decimal places as needed.)

Answer 1

H0: Percentage of the stocks selected by a portfolio manager will increase over 12 months is 46%

H1: Percentage of the stocks selected by a portfolio manager will increase over 12 months is greater than 46%.

Hypothesized proportion, p = 0.46

Observed proportion, = 15/27 = 0.5556

Standard error of proportion, SE =

= 0.0959

Test statistic, z = ( - p) / SE = (0.5556 - 0.46) / 0.0959 = 1.00

P-Value for the test statistic = P(z > 1.00) = 0.159

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that percentage of the stocks selected by a portfolio manager will increase over 12 months is greater than 46%.