uppose a sampling distribution is constructed by selecting random samples of size 9 from a population whose shape is unknown. What will be the shape of the sampling distribution of means? unknown normal skewed uniform (b) Suppose a sampli
(a) Suppose a sampling distribution is constructed by selecting random
What will be the shape of the sampling distribution of means?
- unknown
- normal
- skewed
- uniform
(b) Suppose a sampling distribution is constructed by selecting random samples of size 60 from a population whose shape is skewed.
What will be the shape of the sampling distribution of means?
- uniform
- skewed
- unknown
- normal
(c) Suppose a sampling distribution is constructed by selecting random samples of size 9 from a population whose shape is normal.
What will be the shape of the sampling distribution of means?
- uniform
- skewed
- unknown
- normal
(a)
The sampling distribution of a statistic is known as the probability distribution of all the possible values taken by the statistic which can be selected from the specific population. The sampling distribution of a statistic will be similar for all possible samples of the same size which is selected from the same population. Thus, if a population comes from an unknown distribution with a sample size of less than 30, the shape of the sampling distribution of means will also be unknown.
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(b)
According to the central limit theorem, if the sample size is sufficiently large, i.e., n =30 or >30, the sampling distribution of the mean approaches approximately to normal distribution. In this case, the distribution of the means will always be approximately normal distribution because the sample size 60 is greater than 30.
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