in a 2008 survey people were asked their opinions on astrolo

in a 2008 survey, people were asked their opinions on astrology , very scientific or not

of 1439        75 said very scientific

what is 95% confidence intervalfor the population proportion with this belief

suppose a tv anchor said that 5% of people in the general pop is very scienctific ,, is this plausable?

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.052119527          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.005859312          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    2.33          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.03846733          
upper bound = p^ + z(alpha/2) * sp =    0.065771724          
              
Thus, the confidence interval is              
              
(   0.03846733   ,   0.065771724   ) [ANSWER]

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Yes, it is, because 0.05 is within this interval. [answer]