In: Statistics and Probability
In a statewide opinion poll of a random sample of 300 people, 81 said that they were strongly opposed to having a state lottery. Assuming that the 300 people in the poll are a proper simple random sample, find the 90% confidence interval for the proportion of the state’s population strongly opposed to the lottery.
Solution :
Given that,
n = 900
x = 81
Point estimate = sample proportion = = x / n = 81/900=0.09
1 - = 1- 0.09 =0.91
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z 0.05 = 1.645 ( Using z table )
Margin of error = E Z/2 *(( * (1 - )) / n)
= 1.645 *((0.09*0.91) /900 )
E = 0.016
A 90% confidence interval for population proportion p is ,
- E < p < + E
0.09-0.016 < p < 0.09+0.016
0.074< p < 0.106