The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lea

Question

The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. Table 1 reports the results from a pilot test that measured lead levels in a random sampling of wines.

The BATF wishes to estimate the true average lead level for California wines to within 18 parts per billion at a 90% level of confidence? Based on the BATF's criteria, the number of wine specimens that should be tested is:
Note: you should carry at least 5 decimal precision for any intermediate calculations then round your answer as indicated in the problem

Explanation / Answer

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)=190
Standard deviation( sd )=180
Sample Size(n)=7
Confidence Interval = [ 190 ± t a/2 ( 180/ Sqrt ( 7) ) ]
= [ 190 - 1.943 * (68.03361) , 190 + 1.943 * (68.03361) ]
= [ 57.81071,322.18929 ] ~ [ 57.8,322.2 ]

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