As n increases the sampling distribution of pˆ (p hat) becomes approximately normal.
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.
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.
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
The normal distribution is always continuous.
the standard deviation of the population(sigma)/square root of sampling mean(n)
normal distribution
As n increases the sampling distribution of pˆ (p hat) becomes approximately normal.
normal distribution
No, as you said it is right skewed.
If the population distribution is roughly normal, the sampling distribution should also show a roughly normal distribution regardless of whether it is a large or small sample size. If a population distribution shows skew (in this case skewed right), the Central Limit Theorem states that if the sample size is large enough, the sampling distribution should show little skew and should be roughly normal. However, if the sampling distribution is too small, the sampling distribution will likely also show skew and will not be normal. Although it is difficult to say for sure "how big must a sample size be to eliminate any population skew", the 15/40 rule gives a good idea of whether a sample size is big enough. If the population is skewed and you have fewer that 15 samples, you will likely also have a skewed sampling distribution. If the population is skewed and you have more that 40 samples, your sampling distribution will likely be roughly normal.
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.
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
Z is the standard normal distribution. T is the standard normal distribution revised to reflect the results of sampling. This is the first step in targeted sales developed through distribution trends.
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.
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
The normal distribution is always continuous.