Question

​(a) The shape of the sampling distribution of the sample mean is approximately normal. Is this true or​ false?

Answer 1

The shape of the sampling distribution of the sample mean is approximately normal. This is false.

The statement is true, and it is described by the Central Limit Theorem (CLT). According to the Central Limit Theorem, when you take a sufficiently large number of random samples from a population, the distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution.

This holds true as long as the sample size is large enough (typically n > 30 is considered sufficient for the normal approximation to be valid). In summary, the sampling distribution of the sample mean tends to be approximately normal, making the normal distribution a useful approximation for statistical inference in many cases.

Answer 2

Shape of sampling distribution of sample mean being approx normal or not depends upon sample size.

Explanation:

'The shape of the sampling distribution of the sample mean is approximately normal' might be true or false, depending on sample size.

If the sample size satisfies the condition of being sufficiently large, the shape of sampling distribution of sample mean becomes more bell shaped normally distributed (even more normally distributed than actual population).

Central Limit theorem also states this - Larger the sample size, shape of sampling distribution of sample mean becomes more normally distributed around population mean.