Question

which one of the following statements about the sampling distribution of the sample mean is incorrect?group of answer choicesthe mean of the sampling distribution is equal to the population mean.the sampling distribution is approximately normal whenever the sample size is sufficiently large (n> 30).the standard deviation of the sampling distribution is equal to the population standard deviation.the sampling distribution is generated by repeatedly taking samples of size n, computing the sample means, and then graphing these sample means.

Answer 1

The incorrect statement about the sampling distribution of the sample mean is that the standard deviation of the sampling distribution is equal to the population standard deviation. In fact, it is the population standard deviation divided by the square root of the sample size (n), known as the standard error.

Step-by-step explanation:

The student has asked which statement about the sampling distribution of the sample mean is incorrect. Among the statements given, the incorrect one is: 'The standard deviation of the sampling distribution is equal to the population standard deviation.' This statement is not true because the standard deviation of the sampling distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).

Under the Central Limit Theorem, if the sample is sufficiently large, typically n > 30, the distribution of sample means will be approximately normal, regardless of the population distribution. The mean of the sampling distribution is equal to the population mean. The standard error decreases as the sample size increases, making the distribution of the sample more compact around the population mean.