Question

# We assume that we have selected two independent random samples from populations having proportions $p_1$ and $p_2$ and that $\hat{p}_1=800 / 1,000=.8$ and $\hat{p}_2=950 / 1,000=.95$.Calculate a $95$ percent confidence interval for $p_1-p_2$. Interpret this interval. Can we be $95$ percent confident that $p_1-p_2$ is less than $0$? That is, can we be $95$ percent confident that $p_1$ is less than $p_2$? Explain.

Solutions

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The goal of this task is to compute a confidence interval for $p_1-p_2$ with a $95\%$ confidence interval.

When we have to compute a $100(1-\alpha)\%$ confidence interval for $p_1-p_2$, the formula we have to use is

$\left[ (\^p_1-\^p_2) \pm z_{\alpha/2} \cdot \sqrt{\frac{\^p_1(1-\^p_1)}{n_1}+\frac{\^p_2(1-\^p_2)}{n_2}} \right].$