The electric cooperative needs to know the mean household usage of
electricity by its non-commercial customers in kWh per day. They
would like the estimate to have a maximum error of 0.13 kWh. A
previous study found that for an average family the standard
deviation is 2.1 kWh and the mean is 15.8 kWh per day. If they are
using a 99% level of confidence, how large of a sample is required
to estimate the mean usage of electricity? Round your answer up to
the next integer.
Solution :
Given that,
standard deviation = =2.1
Margin of error = E = 0.13
At 99% confidence level the z is,
= 1 - 99%
= 1 - 0.99 = 0.01
/2 = 0.005
Z/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal (z) table corresponding z value is 2.58 )
sample size = n = [Z/2* / E] 2
n = ( 2.58* 2.1/ 0.13 )2
n =1737
Sample size = n =1737
( when you have z value 3 decimal than Z/2 = 2.576 n=1732)
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