The capacities (in ampere-hours) were measured for a sample of 120 batteries. Th

Question

The capacities (in ampere-hours) were measured for a sample of 120 batteries. The average was 178, and the standard deviation was 14. a) Find a 99% confidence interval for the mean capacity of batteries produced by this method b) An engineer claims that the mean capacity is between 176 and 180 ampere-hours. With what level of confidence can this statement be made? c) Approximately how many batteries must be sampled so that a 99% confidence interval will specify the mean to within plusminus 2 ampere-hours?

Explanation / Answer

a.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=178
Standard deviation( sd )=14
Sample Size(n)=120
Confidence Interval = [ 178 ± t a/2 ( 14/ Sqrt ( 120) ) ]
= [ 178 - 2.618 * (1.278) , 178 + 2.618 * (1.278) ]
= [ 174.654,181.346 ]
c.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 14
ME =2
n = ( 2.58*14/2) ^2
= (36.12/2 ) ^2
= 326.16 ~ 327      

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