Question

True or false? The point estimate for the population mean u of an x distribution is x, computed from a random sample of the x distribution.

O True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution increases as n increases.
O True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution decreases as n increases.
O False. The mean of the x distribution does not equal the mean of the x distribution and the standard error of the x distribution increases as n increases.
O False. The mean of the x distribution does not equal the mean of the x distribution and the standard error of the x distribution decreases as n increases.

Answer 1

The correct answer is "True. The mean of the x distribution equals the mean of the x distribution and the standard error of the x distribution decreases as n increases.

Step-by-step explanation:

True. According to the central limit theorem, the larger the sample, the closer the sampling distribution of the means becomes normal.

The point estimate for the population mean, denoted by u, is the mean of a random sample from the x distribution. The mean of the sampling distribution of the means is approximately the mean of the x distribution.

Additionally, as the sample size increases, the standard error of the x distribution decreases, meaning the standard deviation of the sampling distribution of the means gets smaller and approaches the standard deviation of the x distribution divided by the square root of the sample size (n).

As the sample size n increases, the standard error decreases, allowing the sampling distribution to become more concentrated around the population mean.