A young investor believes that he can beat the market by picking stocks that wil

Question

A young investor believes that he can beat the market by picking stocks that will increase in value. Assume that on average 49% of the stocks selected by a portfolio manager will increase over 12 months. Of the 28 stocks that the young investor bought over the last 12 months, 18 have increased. Can he claim that he is better at predicting increases than the typical portfolio manager? Test at = 0.05.

Calculate the test statistic.

A. The test statistic is __ (Round to two decimal places as needed.)
B. The test statistic cannot be calculated. The conditions for a hypothesis test are not all met.

What is the P­value for the test statistic?
A. The P­value is __ (Round to three decimal places as needed.)
B. The P­value cannot be calculated. The conditions for a hypothesis test are not all met.

What can the investor conclude? Assume = 0.05.
A. He fails to reject the null hypothesis and cannot claim that he is better at predicting increases than the typical portfolio manager, but this conclusion may not be reliable.
B. He rejects the null hypothesis and cannot claim that he is better at predicting increases than the typical portfolio manager, but this conclusion may not be reliable.
C. He fails to reject the null hypothesis and can claim that he is better at predicting increases than the typical portfolio manager, but this conclusion may not be reliable.
D. He rejects the null hypothesis and can claim that he is better at predicting increases than the typical portfolio manager, but this conclusion may not be reliable.
E. No conclusion can be made. The conditions for a hypothesis test are not all met.

Explanation / Answer

Given that,
possibile chances (x)=18
sample size(n)=28
success rate ( p )= x/n = 0.6429
success probability,( po )=0.49
failure probability,( qo) = 0.51
null, Ho:p=0.49  
alternate, H1: p>0.49
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.64286-0.49/(sqrt(0.2499)/28)
zo =1.618
| zo | =1.618
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.618 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.61801 ) = 0.05283
hence value of p0.05 < 0.05283,here we do not reject Ho
ANSWERS
---------------
A. The test statistic is 1.62
A. The P­value is 0.053
A. He fails to reject the null hypothesis and cannot claim that he is better at predicting
increases than the typical portfolio manager, but this conclusion may not be reliable

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