Question

From a survey, 48 out of 50 females voted "no" and 30 out of 50 male voted also for "no". Construct a point estimate for the difference of the population

Answer 1

Estimated proportion of females $\hat{p_1}=\dfrac{48}{50}=0.96$

Estimated proportion of males voters $\hat{p_2}=\dfrac{30}{50}=0.6$

$n_1=50,n_2=50, \alpha=0.05,z_{\frac{\alpha}{2}}=z_{0.025}=1.96$

$p_1-p_2$ : Difference in proportions

The 95% confidence interval interval for $(p_1-p_2)$ is-

     $=(\hat{p_1}-\hat{p_2})\pm z_{0.025}\sqrt{\dfrac{\hat{p_1}(1-\hat{p_1})}{n_1}+\dfrac{\hat{p_2}(1-\hat{p_2})}{n_2}}$

     $=(0.96-0.6)\pm 1.96\sqrt{\dfrac{0.96(1-0.96)}{50}+\dfrac{0.6(1-0.6)}{50}}$

$=0.36\pm 1.96\times\sqrt{0.005568}\\=0.36\pm 0.146\\=(0.2137,0.506)$