Twenty years ago, a very famous psychologist specializing in marriage counseling

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 225 couples who bought her book, she found that 171 of them stayed together. Based on this, compute a 90% 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 90% confidence interval? What is the upper limit of the 90% confidence interval?

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.76          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.028472209          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.046832616          

lower bound = p^ - z(alpha/2) * sp =   0.713167384 [ANSWER]          

upper bound = p^ + z(alpha/2) * sp =    0.806832616   [ANSWER]      
              

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