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Hypothesis Test for a Population Proportion
Many investors and financial analysts believe the Dow Jones Industrial Average (DJ) barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks mal increased in price (The Wall Street Journal, February 1, 2006). On the basis of this claims we can assume that \( 30 \% \) of the stocks traded on the New York Stock Exchang same day.
A sample of 71 stocks traded on the NYSE that day showed that 12 went up.
You are conducting a study to see if the proportion of stocks that went up is is signifi You use a significance level of \( \alpha=0.02 \).
What is the test statistic for this sample? (Report answer accurate to three decimal p test statistic \( = \)
What is the \( p \)-value for this sample? (Report answer accurate to four decimal places.) \( p \)-value \( = \)
The \( \mathrm{p} \)-value is...
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Answer
\( p \)-value: \( 2 * P(Z < -3.088) = 2 * 0.0010 = 0.0020 \)
Step 1 ：n=71, x=12, \( \hat{p} = \frac{12}{71} \), p_0 = 0.3
Step 2 ：Test statistic: \( z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} = \frac{\frac{12}{71} - 0.3}{\sqrt{\frac{0.3 (1 - 0.3)}{71}}} = -3.088 \)
Step 3 ：\( p \)-value: \( 2 * P(Z < -3.088) = 2 * 0.0010 = 0.0020 \)
