Describe the distribution of sample means (i.e., shape, measure of central tendency and variability) for a...

Describe the distribution of sample means (i.e., shape, measure of central tendency and variability) for a sample of n=49 selected from a population with mean of 14 and standard deviation of 7.

Expert Solution

Here, population mean() = 14 , population standard deviation() = 7 and n = 49.

We know that when sample size is large enough (n>30) , the sample means follow a normal distribution in accordancewith the Central limit theorem. Therefore, the shape of the distribution of the sample means will be bell shaped , like a normal curve.

We know that, the mean of the distribution of sample means is equal to the population mean. Therefore, mean of the distribution = = 14

We know that, the standard deviation of the distribution of sample means is equal to the population standard deviation divided by the square root of n. Therefore, standard deviation = / n = 7 / 7 = 1

The sample means are distributed normlly with mean 14 and standard deviation 1.

orchestra answered 2 years ago

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