Question

Twenty years ago, a very famous psychologist specializing in marriage counseling authored a book detailing the way in which she believed spouses should communicate. She is now interested in the proportion of all couples who bought her book who stayed together. For a random sample of

200

couples who bought her book, she found that

166

of them stayed together. Based on this, compute a

95%

confidence interval for the proportion of all couples who bought her book who stayed together. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)

What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?

Answer 1

We have given,              
              
x=166          
n=200          
Estimate for sample proportion=   0.83  
Level of significance is =1-0.95=0.05      
Z critical value(using Z table)=1.96      
              
Confidence interval formula is              


=(0.778,0.882)
              
Lower limit for confidence interval=0.778  
              
Upper limit for confidence interval=0.882