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Hypothesis Test for a Population Proportion
Many investors and financial analysts believe the Dow Jones Industrial Average barometer of the overall stock market. On January 31, 2006, 9 of the 30 stock increased in price (The Wall Street Journal, February 1, 2006). On the basis of claims we can assume that \( 30 \% \) of the stocks traded on the New York Stock ExC same day.
A sample of 79 stocks traded on the NYSE that day showed that 33 went up.
You are conducting a study to see if the proportion of stocks that went up is is si You use a significance level of \( \alpha=0.005 \).
What is the test statistic for this sample? (Report answer accurate to three decim test statistic \( = \)
I
What is the \( p \)-value for this sample? (Report answer accurate to four decimal place \( p \)-value \( = \)
The \( \mathrm{p} \)-value is...
less than (or equal to) \( \alpha \)
Answer
\(z = 1.890 \)
Step 1 ：\(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \)
Step 2 ：\(z = \frac{\frac{33}{79} - 0.3}{\sqrt{\frac{0.3(1-0.3)}{79}}} \)
Step 3 ：\(z = 1.890 \)
