The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 o
ID: 3127526 • Letter: T
Question
The weights of cans of Ocean brand tuna are supposed to have a net weight of 6 ounces. The manufacturer tells you that the net weight is actually a Normal random variable with a mean of 5.95 ounces and a standard deviation of 0.2 ounces. Suppose that you draw a random sample of 42 cans. Suppose the number of cans drawn is doubled. How will the standard deviation of sample mean weight change? Suppose the number of cans drawn is doubled. How will the mean of the sample mean weight change? Consider the statement: 'The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal.'Explanation / Answer
i.
By central limit theorem, as the standard deviation of sample means is inversely proportional to the square root of the sample size, it is
OPTION C: It will decrease by a factor of sqrt(2). [ANSWER]
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ii.
It doesn't change, by central limit theorem.
Hence, OPTION E: It will remain unchanged. [ANSWER]
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iii.
OPTION C: It is a correct statement, and it is a result of the central limit theorem. [ANSWER]
The central limit theorem is the only theorem to support such conclusion.
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