Many investors and financial analysts believe the Dow Jones Industrial Average (

Question

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) provides 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.

1. Formulate null and alternative hypotheses to test the analyst's claim.

H0: p
Ha: p

2. A sample of 50 stocks traded on the NYSE that day showed that 24 went up. What is your point estimate of the population proportion of stocks that went up (to 2 decimals)?


3. Conduct your hypothesis test using = .01 as the level of significance.

Calculate the value of the test statistic (to 2 decimals).


What is the p-value (to 4 decimals)?


Can you conclude that the proportion of stocks going up is not .30?

Explanation / Answer

1. H0: p=0.3 Ha: p not equal to 0.3 2. phat=24/50= 0.48 3. The test statistic is Z=(phat-p)/sqrt(p*(1-p)/n) =(0.48-0.3)/sqrt(0.3*0.7/50) = 2.78 The p-value is 2*P(Z> 2.78)= 0.0054 (check standard normal table) Since the p-value is less than 0.01, we reject Ho. So we can conclude that the proportion of stocks going up is not .30

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