In: Statistics and Probability
A survey of 100 Americans found that 68% said they find it hard to buy holiday gifts that convey their tr ue feelings. Find the 90% confidence interval of the population proportion.
Solution :
Given that,
n = 100
= 0.68
1 - = 1 - 0.68 = 0.32
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.645 * (((0.68 * 0.32) / 100)
= 0.077
A 90% confidence interval for population proportion p is ,
- E < P < + E
0.680 - 0.077 < p < 0.680 + 0.077
0.603 < p < 0.757
(0.603 , 0.757)