The number of absences at a school is studied and the population standard deviat

Question

The number of absences at a school is studied and the population standard deviation of all absences is found to be 1.1.

a. What sample size should be chosen to find the mean number of absences per month of school children to within ±0.2 at a 90% confidence level?

b. What sample size should be chosen to find the mean number of absences per month of school children to within ±0.2 at a 95% confidence level?

c. Comparing the results from (a) and (b) above, what is your observation of how the confidence level changes with the sample size for the same interval?

Explanation / Answer

a.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 1.1
ME =0.2
n = ( 1.64*1.1/0.2) ^2
= (1.8/0.2 ) ^2
= 81.36 ~ 82      
b.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 1.1
ME =0.2
n = ( 1.96*1.1/0.2) ^2
= (2.16/0.2 ) ^2
= 116.21 ~ 117      
c.
increasing the confidence larger the sample size

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