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 53 stocks traded on the NYSE that day showed that 27 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of ?=0.005

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) ??

greater than ??

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 more than 0.3.

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

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

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

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.3
H_A : p > 0.3

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	27	53	0.50943396	0.062946518	3.3271731	0.0004

Hence,

Test statistic = 3.327

p - Value = 0.0004

The p - value is less than (or equal to) ?

Reject the null

The sample data support the claim that the proportion of stocks that went up is is more than 0.3. Option C is correct.