A survey of 1026 people asked What would you do with an unex

A survey of 1,026 people asked: “What would you do with an unexpected tax refund?” Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010). Use Table 1

. a. At 95% confidence, what is the margin of error? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 3 decimal places.)

Construct a 95% confidence interval of the population proportion of people who would pay off debts with an unexpected tax refund. (Use rounded margin of error. Round your answers to 3 decimal places.)

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.47          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.015581641          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.58          
Thus,              

Margin of error = z(alpha/2)*sp =    0.040 [ANSWER]
  
***********************************************      
lower bound = p^ - z(alpha/2) * sp =   0.430          
upper bound = p^ + z(alpha/2) * sp =    0.510      
              
Thus, the confidence interval is              
              
(   0.430   ,   0.510   ) [ANSWER]