Many financial analysts believe the Dow Jones industrial Average (DJIA) provides

Question

Many financial analysts believe the Dow Jones industrial Average (DJIA) provides a good barometer of the overall stock market. On Janury31, 9 of the 30 stocks making up the DJIA increased in price. Based on this fact, a famous financial analyst claimed we can assume that 30% of the stocks traded in the New York Stock Exchange (NYSE) went up the same day. Formulate null and alternative hypotheses to test the claim. A sample of 50 stocks traded on the NYSE that day showed that 24 went up. Conduct a hypothesis test on the original claim using alpha = 0.01 as the level of significance. What is your conclusion?

Explanation / Answer

ans=

Let p be the population proportion, then Null Hypothesis (Ho): p 0.30 Alternative Hypothesis (Ha): p > 0.30 (one-tailed)

Let X be the number of stocks went up, and n be the toal number of stocks traded. Then, X = 24 and n = 50 . Point estimate of population proportion is sample proportion, p-bar= X/n = 24/50 = 0.48.

Test Statistics Z = (p-bar - p) p (1 – p)/n Z = (0.48 – 0.30)/ 0.30 (1-0.30)/50

= 0.18/0.4582/50

=0.18/0.009165

= 19.639

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