Answer:
a) Standard Error = 0.010
b) 95% Confidence Interval = (0.0924 , 0.1316)
Step-by-step explanation:
a) The formula for Standard Error = √Sample Proportion (1 - sample proportion)/n
Standard Error = √p (1 - p)/n
We are told in the question that:
In a random sample of 400 people, 112 agree and 288 disagree. Estimate the standard error using 1000 samples
p = x/n
n = 1000 because we were told to use it instead of 400
x = number for people that agree = 112
p = 112/1000
p = 0.112
Standard Error = √p (1 - p)/n
= √0.112 (1 - 0.112)/1000
= √0.112 × 0.888/1000
= √0.099456 /1000
= √0.000099456
= 0.0099727629
Approximately to 3 decimal places = 0.010
Therefore, the standard error is 0.010
b) The Question above also asked that we solve for the 95% Confidence Interval
The formula =
p ± z × Standard Error
p = 0.112
z score for 95% confidence interval = 1.96
Standard Error = 0.010
Confidence Interval =
0.112 ± 1.96 × 0.010
= 0.112 ± 0.0196
0.112 - 0.0196
= 0.0924
0.112 + 0.0196
0.1316
Therefore, the 95% confidence interval = (0.0924 , 0.1316)
