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 80 stocks traded on the NYSE that day showed that 13 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 $\alpha =0.01$.

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

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

The p-value is...

• less than (or equal to) $\alpha$

• greater than $\alpha$

This test statistic leads to a decision to...

• reject the null

• accept the null

• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0.3.

• There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0.3.

• The sample data support the claim that the proportion of stocks that went up is is less than 0.3.

• There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is less than 0.3.

Answer 1

H0: p = 0.3

Ha: p > 0.3

Sample proportion $\hat{p}$ = 31/80 = 0.3875

Test statistics

z = ( $\hat{p}$ - p) / sqrt ( p ( 1 - p) / n )

= ( 0.3875 - 0.30) / sqrt ( 0.3 ( 1 - 0.3) / 80 )

= 1.708

p-value = P(Z > z)

= P(Z > 1.708)

= 1 - P(Z < 1.708)

= 1 - 0.9562

= 0.0438

Since p-value > 0.001 , fail to reject H0