Please help me answer the question in the picture.. I got answer B, but not 100%

Question

Please help me answer the question in the picture..

I got answer B, but not 100% sure...

A new brand of chocolate bar is being market tested. Five hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below. What is the 95% confidence interval for the proportion of consumers that liked the new chocolate bar? a. 0.47 plusminus 0.0223 b. 0.47 plusminus 0.0437 c. 0.47 plusminus 1.96 d. 0.47 plusminus 0.53 e. None of these

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n = 235/500 =   0.47          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.022320394          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          

Thus,              

Margin of error = z(alpha/2)*sp =    0.043747169 = 0.0437          

Hence, the confidence interval is

OPTION B: 0.47 +/- 0.0437 [ANSWER]

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