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(Confidence Interval for proportions) A survey of 50 first-time white-water cano

ID: 3380980 • Letter: #

Question

(Confidence Interval for proportions) A survey of 50 first-time white-water canoers showed that 23 did not want to repeat the experience. A) find a 90% confidence interval of the true proportion of canoers who did not wish to canoe the rapids a second time. (Hint: critical value can be found in the Z-table by using probability 0.95). (Confidence Interval for proportions) A survey of 50 first-time white-water canoers showed that 23 did not want to repeat the experience. A) find a 90% confidence interval of the true proportion of canoers who did not wish to canoe the rapids a second time. (Hint: critical value can be found in the Z-table by using probability 0.95). A survey of 50 first-time white-water canoers showed that 23 did not want to repeat the experience. A) find a 90% confidence interval of the true proportion of canoers who did not wish to canoe the rapids a second time. (Hint: critical value can be found in the Z-table by using probability 0.95).

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.46          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.070484041          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.34406407          
upper bound = p^ + z(alpha/2) * sp =    0.57593593          
              
Thus, the confidence interval is              
              
(   0.34406407   ,   0.57593593   ) [answer]