The Apgar score was developed as a tool for assessing the we

The Apgar score was developed as a tool for assessing the well-being of newborns a few minutes after delivery.Low Apgar scores (< 7) are associated with neonatal death.In a 2014 study of 125 randomly selected teen mothers, 16 of their infants had 1-minute Apgar scores under 7.

Construct a 90% confidence interval for the proportion of infants of teen mothers that have 1-minute Apgar scores under 7. For full credit, state all values needed for the formula you choose, including the critical value(s), state the final confidence interval and provide an interpretation.                                                              

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.128          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.029881901          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.049151353          
lower bound = p^ - z(alpha/2) * sp =   0.078848647          
upper bound = p^ + z(alpha/2) * sp =    0.177151353          
              
Thus, the confidence interval is              
              
(   0.078848647   ,   0.177151353   )

Thus, we are 90% confident that the true proportion of infants of teen mothers that have 1-minute Apgar scores under 7 is between 0.078848647 and 0.177151353. [CONCLUSION]