For this problem, carry at least four digits after the decimal in your calculati

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a marketing survey, a random sample of 720 women shoppers revealed that 634 remained loyal to their favorite supermarket during the past year (i.e., did not switch stores).

(a) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate for p. (Round your answer to four decimal places.)
= 0.8806

(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

lower limit 0.857 upper limit 0.904

(c) What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.8806 [ANSWER]

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B)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.012086348          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
      
lower bound = p^ - z(alpha/2) * sp =   0.856866748          
upper bound = p^ + z(alpha/2) * sp =    0.904244363          
              
Thus, the confidence interval is              
              
(   0.856866748   ,   0.904244363   )
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C)

Margin of error = z(alpha/2)*sp =    0.023688808   = 0.024 [ANSWER]

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