3. Many investors and financial analysts believe the Dow Jones Industrial Averag

Question

3. 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. a. Formulate null and alternative hypotheses to test the analyst’s claim. b. 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? c. Conduct your hypothesis test using =.01 as the level of significance. What is your conclusion?

Explanation / Answer

ANS=

X/n = p(hat)~ N[p p(1-p)/n]
p(hat) = 24/50
Ho: p = c = 0.3
Ha: p not equal 0.3 (two tailed test)

Test Statistic:
Z = p(hat) - c / sqrt[c(1-c)/n]
Z = 24/50 - 0.3 / sqrt [(0.3*0.7)/50]
Z = 9/50 / 0.06481
Z = 2.78 (2dp)

Significance level = 0.01
divide by 2 since it is 2 tailed test
Z (SL) = 2.575

P-value:P(|Z|>2.78) = 2*P(Z>2.78)
= 2*0.0027
=0.0054

P-value is very close to 0 and shows that there is a large error/doubt involved.

From the test statistic and p-value we can conclude that we reject the null hypothesis. There is enough evidence to doubt the analyst's claim.

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