Question
In: Statistics and Probability
We would like to know: "What percentage of college students drink alcohol every day?" In a...
We would like to know: "What percentage of college students drink alcohol every day?" In a random sample of 500 students, 75 said they drink alcohol every day. Use the data to construct a 95% confidence interval to answer to the question. You MUST show your work to receive full credit.
Solutions
Expert Solution
Solution :
Given that,
n = 500
x = 75
Point estimate = sample proportion = 
= x / n = 0.15
1 -
= 0.85
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z
/ 2 * 
* (1 -
)) / n)
= 1.96 * (
= 0.031
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.15 - 0.031 < p < 0.15 + 0.031
0.119 < p < 0.181
( 0.119 , 0.181 )
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