Question

The point estimate for the proportion of 16-kbit dynamics RAMs that function correctly for at least 1000 hours based on a sample size 100 is .91. Find a 95% confidence interval on p.

Answer 1

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} = 1.96.$

The corresponding confidence interval is computed as shown below:

$$CI(Proportion)=(\hat{p}-z_c\times\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}},$$

$$\hat{p}+z_c\times\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})$$

$$=(0.91-1.96\times\sqrt{\dfrac{0.91(1-0.91)}{100}},$$

$$0.91+1.96\times\sqrt{\dfrac{0.91(1-0.91)}{100}})$$

$$=(0.854,0.966)$$

Therefore, based on the data provided, the 95% confidence interval for the population proportion is $0.854 < p < 0.966,$ which indicates that we are 95% confident that the true population proportion $p$ is contained by the interval $(0.854, 0.966).$