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Mean weight of whole from sample size

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"A fish wholesaler has a catch of several thousand lobsters. A prospective buyer selected 40 at random and obtained the following weights in ounces:

21.3, 21.1, 21.4, 18.8, 20.2, 19.3, 19.1, 18.3, 19.9, 22.0,
20.6, 20.7, 21.9, 20.1, 17.1, 19.3, 21.2, 18.4, 21.0, 21.6,
16.5, 18.9, 17.4, 20.8, 18.5, 18.1, 21.1, 19.3, 21.5, 20.1,
21.8, 20.2, 19.7, 18.9, 19.5, 20.0, 18.7, 21.6, 20.9, 21.5,

The prospective buyer will purchase the entire catch if it can be shown that the mean weight (of the entire catch) exceeds 19.9 ounces. Should he purchase the entire catch?"

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Solution Summary

Mean weight of whole from sample size is examined.

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Weight, X X - X̅ (X - X̅)^2
21.3 1.3425 1.80230625
21.1 1.1425 1.30530625
21.4 1.4425 2.08080625
18.8 -1.1575 1.33980625
20.2 0.2425 0.05880625
19.3 -0.6575 0.43230625
19.1 -0.8575 0.73530625
18.3 -1.6575 2.74730625
19.9 -0.0575 0.00330625
22 2.0425 4.17180625
20.6 0.6425 0.41280625
20.7 0.7425 0.55130625
21.9 1.9425 3.77330625
20.1 0.1425 0.02030625
17.1 -2.8575 8.16530625
19.3 -0.6575 0.43230625
21.2 1.2425 1.54380625
18.4 -1.5575 2.42580625
21 1.0425 1.08680625
21.6 ...

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