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 73 stocks traded on the NYSE that day showed that 11 went up. You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of ? = 0.01 .

What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = -2.784 Correct

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

Answer 1

alpha = 0.01
p.hat = 11/73
p.0=0.3
z = (p.hat-p.0)/sqrt(p.0*(1-p.0)/73) =-2.783911
z.alpha = qnorm(0.01/2,lower.tail = TRUE) # two tailed test

=-2.575829

z < z.alpha

p.value = pnorm(z,lower.tail = TRUE) =  0.005370769

p.value < alpha

we reject H_0 based on p.value and test statistics.