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Answer:
The mean is zero and the standard deviation is one.
Correct, since the sample mean is not always defined by a distribution with mean 0 and deviation 1. Since the normal standard distribution is not always representative of the sample mean dsitribution
Step-by-step explanation:
For this case we want to analyze the distribution of the sample mean given by:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Let's analyze one by one the possible options:
The distribution of the values is obtained by repeated sampling.
False, for this case we assume that the data of each observation [tex] X_i[/tex] , [tex] i =1,2,...,n[/tex] is obtained from a repated sampling method
The samples are all of size n.
False, for this case we assume that the sample mean is obtained from n data values
The samples are all drawn from the same population.
False, for this case we assume that the data comes from the same distribution
The mean is zero and the standard deviation is one.
Correct, since the sample mean is not always defined by a distribution with mean 0 and deviation 1. Since the normal standard distribution is not always representative of the sample mean dsitribution
The mean is zero and the standard deviation is one.
It is not characteristic of the sampling distribution of a sample mean.
In the Sampling Distribution of the Sample Mean , If repeated random samples of a given size n are taken from a population .where the population mean is μ and the population standard deviation is σ .then the mean of all sample means is population mean μ .
Characteristic of Sampling Distribution ,
- The overall shape of the distribution is symmetric and approximately normal.
- There are no outliers or other important deviations from the overall pattern.
- The center of the distribution is very close to the true population mean
So, The mean is zero and the standard deviation is one in sampling distribution is not any mandatory condition.
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