The mean of the sampling distribution is the population mean.
This is the Central Limit Theorem.
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
It is the sampling distribution of that variable.
A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
the standard deviation of the population(sigma)/square root of sampling mean(n)
This is the Central Limit Theorem.
Also normally distributed.
Thanks to the Central Limit Theorem, the sampling distribution of the mean is Gaussian (normal) whose mean is the population mean and whose standard deviation is the sample standard error.
a) T or F The sampling distribution will be normal. Explain your answer. b) Find the mean and standard deviation of the sampling distribution. c) We pick one of our samples from the sampling distribution what is the probability that this sample has a mean that is greater than 109 ? Is this a usual or unusual event? these are the rest of the question.
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
A set of probabilities over the sampling distribution of the mean.
NO
i dont no the answer
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
It will be the same as the distribution of the random variable itself.
It is the sampling distribution of that variable.
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.