Question

In: Statistics and Probability

1. A )When a sample of n observations are selected from population that has a mean...

1. A )When a sample of n observations are selected from population that has a mean equal to μ, then the sampling distribution of sample means will have a mean...

that may be larger or less than μ , depending on the size of the sample, n


greater than μ

less than μ

equal to μ
b) When a sample of n observations are selected from population that has a mean equal to μ and a standard deviation equal to σ then the sampling distribution of sample means will have a standard deviation ...

less than σ

greater than σ

equal to σ

that may be greater than or less than σ , depending on the size of the sample, n

C) When a sample of 40 observations are selected from a uniform population that has a mean equal to μ and a standard deviation equal to σ then the sampling distribution of sample means will have a shape that is ...

uniform


skewed right


skewed left


normal

Solutions

Expert Solution

Ans.

Mean

The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ. The symbol μM is used to refer to the mean of the sampling distribution of the mean. Therefore, the formula for the mean of the sampling distribution of the mean can be written as:

μM = μ

A)equal to μ

B)depending on the size of the sample n

because formula for Sample standard deviation is given by its clearly say that its depends on sample size n

σx = σ / sqrt(n).

C)normal.

Show for dummy example:

shows a side-by-side comparison of a histogram for the original population and a histogram for this distribution. Whereas the distribution of the population is uniform, the sampling distribution of the mean has a shape approaching the shape of the familiar bell curve. This phenomenon of the sampling distribution of the mean taking on a bell shape even though the population distribution is not bell-shaped happens in general. Here is a somewhat more realistic example.

Figure 6.1 Distribution of a Population and a Sample Mean

orchestra answered 1 year ago
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