In: Statistics and Probability
A survey of 547 Americans was asked if commuting to work was stressful. 24% of them said that it was. Find a 95% confidence interval for the proportion of American that find commuting to work stressful.
Solution :
Given that,
n = 547
Point estimate = sample proportion = = 0.24
1 - = 1-0.24=0.76
At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 (((0.24*0.76) / 547)
= 0.036
A 95% confidence interval for proportion p is ,
- E < p < + E
0.24-0.036 < p <0.24+0.036
0.204<P<0.276