Question 346570: Question A is if variable is normally distributed, mean 35, standard deviation 42, identify the sampling distribution of the sample mean for sample of size 9. Question B is: Can you answer part (a) if the distribution of the variable under consideration is unknown. My response is: No because the sample is size 9 – since the distribution of the population is not specified, we need a sample size of at least 30 to apply.
Can you tell me if my response is correct? Thank you for any help you can give me.
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Question A is if variable is normally distributed, mean 35, standard deviation 42, identify the sampling distribution of the sample mean for sample of size 9
--
if the underlying distribution is known to be Normal with mean=35 and stdev=42, then the distribution for the sample mean will be normal with mean =35 and standard error=stdev/sqrt(n)=42/sqrt(9)=14
===
Can you answer part (a) if the distribution of the variable under consideration is unknown
--
if the underlying distribution is unknown, you are correct that the distribution of the sample mean is unknown as long as the sample sizes are small, you need samples larger than 30 (actually the large the better) to begin relying on the central limit theorem to insure that the resulting distribution for the sample mean is normal
|
|
|
