Question
In: Statistics and Probability
An investigator wants to estimate the proportion of freshman at his university who currently smoke cigarettes....
An investigator wants to estimate the proportion of freshman at his university who currently smoke cigarettes. How many freshman should be involved in the study to ensure that a 90% confidence interval estimate of the proportion is within 0.04 of the true proportion?
Solutions
Expert Solution
Solution :
Given that,
= 0.5
1 -
= 0.5.
margin of error = E = 0.04
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645 ( Using z table )
Sample size = n = (Z
/2
/ E)2 *
* (1 -
)
= (1.645 / 0.04)2 * 0.5 * 0.5
=422.816
Sample size = 423
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