Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.A quality control manager initially plans to take a simple random sample of size n from the production line.If he were to double his sample size (to 2n),by what factor would the standard deviation of the sampling distribution of change?
A)1/2

Question

Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.A quality control manager initially plans to take a simple random sample of size n from the production line.If he were to double his sample size (to 2n),by what factor would the standard deviation of the sampling distribution of  change?
A)1/2

Quizplus · Accepted Answer

When the sample size is doubled from n to 2n, the standard deviation of the sampling distribution of the sample mean is divided by the square root of 2n/n, which simplifies to the square root of 2. Therefore, the standard deviation will be multiplied by 1.414 or approximately 1.4. So, the answer is B.

Chocolate Bars Produced by a Certain Machine Are Labeled 8