In: Statistics and Probability
A random sample of 150 companies found that 75 of them use social-media tools and technologies. Determine the LOWER confidence limit (LCL) for an 80% confidence interval for the population proportion.
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 75 / 150 = 0.500
1 -
= 1 - 0.500 = 0.5
Z
= 0.842
Margin of error = E = Z *
((
* (1 -
)) / n)
= 0.842 * (((0.500
* 0.5) /150 )
Margin of error = E = 0.034
A 80% lower confidence interval for population proportion p is ,
- E
0.500 - 0.034
0.466
Lower confidence limit: 0.466