Question

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 69 stocks traded on the NYSE that day showed that 25 went up. You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α = 0.05 α = 0.05 .

What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value = The p-value is... less than (or equal to) α α greater than α α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3. There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is more than 0.3. The sample data support the claim that the proportion of stocks that went up is is more than 0.3. There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.

Answer 1

null Hypothesis:               Ho:   p		=	0.300
alternate Hypothesis:    Ha: p		>	0.300
for 0.05 level with right tailed test , critical z=			1.645
Decision rule :   reject Ho if test statistic z > 1.645
sample success x   =		25
sample size          n    =		69
std error   se =√(p*(1-p)/n) =		0.0552
sample proportion p̂ = x/n=		0.3623
test stat z =(p̂-p)/√(p(1-p)/n)=		1.130
p value                          =		0.1293

The p-value is greater than α This test statistic leads to a decision to  fail to reject the null As such, the final conclusion is that

here is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.