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?

Answer 1

1) H0: p=0.3

Ha: p≠0.3

2) 0.48

3)•2.78

•0.0054. So, we reject H0.

• No, we cannot conclude

•

Explanation:

1) To formulate the null and alternative hypothesis:

• Null hypothesis:

`H_0: p=0.3`

•Alternative hypothesis:

Ha: p≠0.3

2) Point estimate of the population proportion stocks that went up:

Since sample is 50 stocks and 24 went up, we have phat as:

`phat = (24)/(50) = 0.48`

3) • Hypothesis test using 0.01 as level of significance:

Test statistic =

`Z = \frac{phat-p}{\sqrt{(p*(1-p))/(n)}}`

`= \frac{0.48-0.3}{\sqrt{(0.3*0.7)/(50)}}`

= 2.78

•Using standard normal table

P value =

2*(P>2.78) = 0.0054

• The p value (0.0054) is less than level of significance (0.01), we reject null hypothesis H0.

• No, we cannot conclude that the proportion of stocks going up is not .30