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 98% level of confidence? Based on the BATF's criteria, the number of wine specimens that should be tested is:

Table 1: Descriptive statistics for the lead in wine study Variable n mean Std.Dev SEmean lead 15 230 120 30.98

Explanation / Answer

Here sample size is small so we use the formula as,

n = [ (Zc * sigma) / E ]2

where Zc is the z-critical value.

sigma is the standard deviation = 120

E is margin of error = 18

c = confidence level = 98% = 0.98

We can find Zc by using EXCEL.

syntax is,

=NORMSINV(probability)

where probability = 1 - a/2

a = 1 - c

Zc = 2.33

n = [(2.33*120) / 18 ]2 = 15.532 = 241.2844 = 241

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