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. Part i) Suppose the number of cans drawn is doubled. How will the standard deviation of sample mean weight change? A. It will increase by a factor of 2.
B. It will increase by a factor of square root of 2.
C. It will decrease by a factor of square root of 2.
D. It will decrease by a factor of 2.
E. It will remain unchanged. Part ii) Suppose the number of cans drawn is doubled. How will the mean of the sample mean weight change? A. It will increase by a factor of 2.
B. It will increase by a factor of square root of 2.
C. It will decrease by a factor of square root of 2.
D. It will decrease by a factor of 2.
E. It will remain unchanged. Part iii) Consider the statement: ‘The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal.’ A. It is a correct statement, and it is a result of the Central Limit Theorem.
B. It is a correct statement, but it is not a result of the Central Limit Theorem.
C. It is an incorrect statement. The distribution of the mean weight of the sample is not Normal.