In: Statistics and Probability
In a survey of 1470 adults from the United States, 221 said that of all the presidents in our nations history, they most admired Abraham Lincoln.
Use the information above to answer the following.
1) Identify x:
2) Identify n:
3) Identify pˆp^
4) Identify qˆq^
Construct a 90% confidence interval for the proportion of adults who say that of all the presidents in our nation's history , they most admire Abraham Lincoln.
5) Identify the zα/2zα/2
6) Identify the Error (E):
7) Write the confidence interval use the values you found above:
Solution :
Given that,
n = 1470
x = 221
Point estimate = sample proportion = = x / n =221/1470=0.150
1 - = 1-0.150 =0.85
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645 ( Using z table )
Margin of error = E Z/2 *(( * (1 - )) / n)
= 1.645 *((0.15*0.85) /1470 )
E = 0.015
A 90% confidence interval is ,
- E < p < + E
0.15-0.015 < p < 0.15+0.015
0.135< p < 0.165
(0.135 , 0.165)