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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.
What else can I help you with?
When the population standard deviation is not known the sampling distribution is a?
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.
What is the standard error of the sampling distribution equal to when you do not know the population standard deviation?
You calculate the standard error using the data.
The standard deviation of the distribution of means is also known as the population standard deviation?
Yes.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
How do you calculate Z and T scores?
z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)
When the population standard deviation is known the sampling distribution is a?
normal distribution
When the population standard deviation is not known the sampling distribution is a?
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.
When the population standard deviation is known the sampling distribution is known as what?
normal distribution
When the population standard deviation is not know the sampling distribution is a?
When the population standard deviation is not known, the sampling distribution of the sample mean is typically modeled using the t-distribution instead of the normal distribution. This is because the t-distribution accounts for the additional uncertainty introduced by estimating the population standard deviation from the sample. As the sample size increases, the t-distribution approaches the normal distribution, making it more appropriate for larger samples.
What is the standard error of the sampling distribution equal to when you do not know the population standard deviation?
You calculate the standard error using the data.
The standard deviation of the distribution of means is also known as the population standard deviation?
Yes.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
What is a t distribution?
The t distribution is a probability distribution that is symmetric and bell-shaped, similar to the normal distribution, but has heavier tails. It is used in statistics, particularly for small sample sizes, to estimate population parameters when the population standard deviation is unknown. The t distribution accounts for the additional uncertainty introduced by estimating the standard deviation from the sample. As the sample size increases, the t distribution approaches the normal distribution.
What is the sampling distribution when the standard deviation is known?
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.
What is the standard deviation of a standard normal distribution?
The standard deviation in a standard normal distribution is 1.
When to use z or t-distribution?
If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution
What information do you need to calculate a probability with a normal distribution?
Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.
