In: Statistics and Probability
In a random sample of 1200 potential buyers, 376 indicated that they would consider purchasing a hybrid vehicle. Estimate the proportion of people that would consider purchasing a hybrid vehicle at a 96% confidence level. Critical Value: Your answer should contain three decimal places Confidence Interval: ( , ) Keep your answers as decimals (not percentages) and round your answers to 3 decimal places.
Solution :
Given that,
n = 1200
x = 376
Point estimate = sample proportion =
= x / n = 376/1200=0.313
1 -
= 1-0.313=0.687
At 96% confidence level
= 1 - 96%
= 1 - 0.96 =0.04
/2
= 0.02
Z/2
= Z0.02= 2.054 ( Using z table )
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 2.054 (((0.313*687)
/1200 )
= 0.027
A 95% confidence interval f is ,
- E < p <
+ E
0.313-0.027 < p < 0.313+0.027
0.289<p<0.340
(0.289 , 0.340)