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 60 stocks traded on the NYSE that day showed that 8 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=0.01.

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) α

• greater than α

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

Solution :

This is the left tailed test .

n = 60

x = 8

= x / n = 8 / 60 = 0.1333

P₀ = 0.30

1 - P₀ = 0.70

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1333 - 0.30 / [(0.30 * 0.30) / 60]

= -2.817

Test statistic = -2.817

P(z < -2.817) = 0.0024

P-value = 0.0024

= 0.01

P-value <

Reject the null hypothesis .

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