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Test for a Population Proportion
in brokerage firm executive claimed that \( 10 \% \) of investors are currently confident of \( m e \) tment goals. An XYZ Investor Optimism Survey, conducted over a two week period, founo of 700 people, \( 16 \% \) of them said they are confident of meeting their goals.
claim that the proportion of people who are confident is larger than \( 10 \% \) at the 0.10 significc
I and alternative hypothesis would be:
Answer
Step 3: Determine the critical value \(z_\alpha\) corresponding to the significance level \(\alpha = 0.10\) and compare it with the calculated test statistic to make a decision.
Step 1 ：Step 1: Define the null hypothesis \(H_0\) and alternative hypothesis \(H_1\). \(H_0: p = 0.10\) and \(H_1: p > 0.10\)
Step 2 ：Step 2: Calculate the test statistic: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\) with \(\hat{p}=0.16\), \(p_0=0.10\), and \(n=700\)
Step 3 ：Step 3: Determine the critical value \(z_\alpha\) corresponding to the significance level \(\alpha = 0.10\) and compare it with the calculated test statistic to make a decision.
