The table to the right shows the results of a survey in which 2571 adults from C

Question

The table to the right shows the results of a survey in which 2571 adults from Country A, 1118 adults from Country B, and 1090 adults from Country C were asked if human activity contributes to global warming. Complete parts (a), (b), and (c). Adults who say that human activity contributes to global warming Country Upper A 68 % Country Upper B 89 % Country Upper C 91 %

(a) Construct a 99 % confidence interval for the proportion of adults from Country Upper A who say human activity contributes to global warming. left parenthesis nothing comma nothing right parenthesis (Round to three decimal places as needed.)

(b) Construct a 99 % confidence interval for the proportion of adults from Country Upper B who say human activity contributes to global warming. left parenthesis nothing comma nothing right parenthesis (Round to three decimal places as needed.)

(c) Construct a 99 % confidence interval for the proportion of adults from Country Upper C who say human activity contributes to global warming. left parenthesis nothing comma nothing right parenthesis (Round to three decimal places as needed.)

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.68          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.0091998          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.023697116          
lower bound = p^ - z(alpha/2) * sp =   0.656302884          
upper bound = p^ + z(alpha/2) * sp =    0.703697116          
              
Thus, the confidence interval is              
              
(   0.656302884   ,   0.703697116   ) [ANSWER]

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

b)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.89          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.009357729          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.024103911          
lower bound = p^ - z(alpha/2) * sp =   0.865896089          
upper bound = p^ + z(alpha/2) * sp =    0.914103911          
              
Thus, the confidence interval is              
              
(   0.865896089   ,   0.914103911   )

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

c)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.91          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.008668196          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.022327792          
lower bound = p^ - z(alpha/2) * sp =   0.887672208          
upper bound = p^ + z(alpha/2) * sp =    0.932327792          
              
Thus, the confidence interval is              
              
(   0.887672208   ,   0.932327792   ) [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.