Homework SourseThe table shows the results of a survey in which separate sa
The table shows the results of a survey in which separate samples of 400 adults each from the east, south, midwest, and west were asked if traffic congestion is a serious problem in their community. Complete parts (a) and (b) (a) construct a 95% confidence interval for the proportion of adults from the midwest who say traffic congestion is a serious problem. (___, ____) (b) Construct a 95% confidence interval for the proportion of adults from the west who say traffic congestion is a serious problem. (____, ____) east - 36% south - 33% midwest - 25% west - 53%
Solution
A)
Note that
p^ = point estimate of the population proportion = x / n = 0.25
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.021650635
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.042434465
lower bound = p^ - z(alpha/2) * sp = 0.207565535
upper bound = p^ + z(alpha/2) * sp = 0.292434465
Thus, the confidence interval is
( 0.207565535 , 0.292434465 ) [ANSWER]
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b)
Note that
p^ = point estimate of the population proportion = x / n = 0.33
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.023510636
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.04608
lower bound = p^ - z(alpha/2) * sp = 0.28392
upper bound = p^ + z(alpha/2) * sp = 0.37608
Thus, the confidence interval is
( 0.28392 , 0.37608 ) [ANSWER]
