In a random sample of 400 measurements, 227 of the

Solution:

Step 1 of 2:

 In a sample of 400 measurements, 227 measurements possess the characteristics of interest, A.

1. The claim is to use 95% confidence interval to estimate the true proportion p of measurements in the population with characteristic A.

the sample size large enough if n15 and n15

The point estimate of p is  =

                                              =

                                             = 0.5675.

Then, n= 400(0.5675)

               = 227

          n= 400(0.4325)

         =173.

Since both are greater than 15, the sample size is sufficiently  large to conclude that the normal approximation is reasonable.

For confidence interval 0.95

= 0.05, = 0.025 and = 1.96 ( from are under normal curve table)

Then,

     0.5675  1.96

   0.5675   0.04855

(0.5189, 0.6160)

Hence, we are 95 % confident that the true proportion of all the true proportion p of measurements in the population with characteristic A is between 0.5189 and 0.6160.