The table to the right shows the results of a survey in which 400 adults from th

Question

The table to the right shows the results of a survey in which 400 adults from the East, 400 adults from the South, 400 adults from the Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts (a) and (b).

Adults who say that traffic congestion is a serious problem

East 36%

South 32%

Midwest 26%

West 57%

(a) Construct a 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem. The 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem is left parenthesis is? (Round to three decimal places as needed.)

(b) Construct a 99% confidence interval for the proportion of adults from the MidwestMidwest who say traffic congestion is a serious problem. Is it possible that these two proportions are equal? Explain your reasoning. The 99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem is ? (Round to three decimal places as needed.)

Is it possible that these two proportions are equal?

a.)No, because the 99% confidence interval for the West does not overlap with the 99% confidence interval for the Midwest.

b.)Yes, because the 99% confidence interval for the West overlaps with the 99% confidence interval for the Midwest.

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.57          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.024753788          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.063761531          
lower bound = p^ - z(alpha/2) * sp =   0.506238469          
upper bound = p^ + z(alpha/2) * sp =    0.633761531          
              
Thus, the confidence interval is              
              
(   0.506238469   ,   0.633761531   ) [ANSWER]

**********************

b)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.26          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.021931712          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.056492347          
lower bound = p^ - z(alpha/2) * sp =   0.203507653          
upper bound = p^ + z(alpha/2) * sp =    0.316492347          
              
Thus, the confidence interval is              
              
(   0.203507653   ,   0.316492347   ) [ANSWER]

*************************

c)

These two intervals do not overlap, so

OPTION A: a.)No, because the 99% confidence interval for the West does not overlap with the 99% confidence interval for the Midwest. [ANSWER, A]

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