6. Many investors and financial analysts believe the Dow Jones Industrial Averag
ID: 3351745 • Letter: 6
Question
6. 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 61 stocks traded on the NYSE that day showed that 6 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 =0.02=0.02.
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...
A less than (or equal to)
B greater than
This test statistic leads to a decision to...
A reject the null
B accept the null
C fail to reject the null
As such, the final conclusion is that...
A There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0.3.
B 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.
C The sample data support the claim that the proportion of stocks that went up is is less than 0.3.
D There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is less than 0.3.
Explanation / Answer
The statistical software output for this problem is:
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.3
HA : p < 0.3
Hypothesis test results:
Hence,
Test statistic = -3.437
P - value = 0.0003
The p - value is less than or equal to
This test statistic leads to a decision to reject the null
Conclusion: The sample data support the claim that the proportion of stocks that went up is is less than 0.3. Option C is correct.
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 6 61 0.098360656 0.058673869 -3.4366124 0.0003Related Questions
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