In: Statistics and Probability
Fear of breast cancer. A recent survey of 1000 American women ages 45-64 asked them what medical condition they feared the most. 61% said that they feared breast cancer the most. Construct a 95% confidence interval for the population proportion of women who most feared breast cancer. Then Interpret the confidence interval.
Solution :
Given that,
n = 1000
Point estimate = sample proportion =
=0.61
1 -
= 1-0.61=0.39
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 (((0.61*0.39)
/ 1000)
E= 0.0302
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.61 -0.0302 < p <0.61+< 0.0302
0.5798< p <0 .6402
The 95% confidence interval for the population proportion p is : 0.5798,0 .6402