Question

A young investor believes that he can beat the market by picking stocks that will increase in value. Assume that on average 47 % 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, 19 have increased. Can he claim that he is better at predicting increases than the typical portfolio​ manager? Test at alphaequals0.05. What are the null and alternative hypotheses for this​ test? A. H0​: pequals0.47 vs. HA​: pless than0.47 B. H0​: pequals0.47 vs. HA​: pgreater than0.47 C. H0​: pequals0.47 vs. HA​: pnot equals0.47 D. H0​: pnot equals0.47 vs. HA​: pequals0.47 Calculate the test statistic. A. The test statistic is nothing. ​(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​ P-value for the test​ statistic? A. The​ P-value is nothing. ​(Round to three decimal places as​ needed.) B. The​ P-value cannot be calculated. The conditions for a hypothesis test are not all met. What can the investor​ conclude? Assume alphaequals0.05. A. 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. B. 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. 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 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. E. No conclusion can be made. The conditions for a hypothesis test are not all met.

Answer 1

null Hypothesis:               Ho:   p		=	0.470
alternate Hypothesis:    Ha: p		>	0.470

sample success x   =		19
sample size          n    =		28
std error   se =√(p*(1-p)/n) =		0.0943
sample proportion p̂ = x/n=		0.6786
test stat z =(p̂-p)/√(p(1-p)/n)=		2.21

p value                          =

0.014

  B. 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.