Question

With the rise of stock market, an investment advisor believes that the percentage of investors who are risk–taking (i.e., trying to take risk in their investment decisions) is greater than 80%. A survey of 115 investors found that 95 of them were risk-taking. Formulate and test the appropriate hypotheses to determine whether his belief can be confirmed (significance level of 5%).

please show work on excel!!!

Answer 1

null Hypothesis:               Ho:   p		=	0.800
alternate Hypothesis:    Ha: p		>	0.800
for 0.05 level with right tailed test , critical z=			1.645 #(use normsinv(0.95) function of excel)
Decision rule :   reject Ho if test statistic z > 1.645

sample success x   =		95
sample size          n    =		115
std error   se =√(p*(1-p)/n) = sqrt(0.8*0.2/115)=		0.0373
sample proportion p̂ = x/n=95/115=		0.8261
test stat z =(p̂-p)/√(p(1-p)/n)=(0.8261-0.80)/0.0373=		0.700
p value                          =		0.2420 # use 1-normsdist(0.70) function of excel(

since p value is greater than 0.05 level, we fail to reject null hypothesis

we do not have sufficient evidence at 0.05 level to conclude that percentage of investors who are risk–taking (i.e., trying to take risk in their investment decisions) is greater than 80%.