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 69 stocks traded on the NYSE that day showed that 17 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 α=0.001α=0.001.

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) αα
• greater than αα

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

Let p denotes the true proportion of stocks that went up.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at α=0.001 if P-value < 0.001

Now,

The value of the test statistic

P-value

P-value is greater than α = 0.001

This test statistic leads to a decision to fail to reject the null hypothesis.

As such, the final conclusion is that

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