For this problem carry at least four digits after the decima

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 69 professional actors, it was found that 44 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.637681159   [ANSWER]

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b)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.057865899          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
      
lower bound = p^ - z(alpha/2) * sp =   0.524266081          
upper bound = p^ + z(alpha/2) * sp =    0.751096238 [ANSWER]