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In: Statistics and Probability

Suppose Diane and JackJack are each attempting to use a simulation to describe the sampling distribution...

Suppose Diane and JackJack are each attempting to use a simulation to describe the sampling distribution from a population that is skewed right with mean 7070 and standard deviation 1010. Diane obtains 1000 random samples of size nequals=44 from the population, finds the mean of the means, and determines the standard deviation of the means. JackJack does the same simulation but obtains 1000 random samples of size nequals=3030 from the population

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Expert Solution

According to central limit theorem, if sample size n is large (n > 30) then we can say that the sampling distribution of sample mean is approximately normally distributed with mean and standard deviation

Here n = 44 > 30

So we can say that sampling distribution of sample mean is approximately normally distributed with

Mean of sample mean =

Standard deviation of sample mean

= 152.2632

Mean of sample mean = 7070

Standard deviation of sample mean = 152.2632

If n = 3030 then

Mean of sample mean =

Standard deviation of sample mean

= 18.3485                                      (Round to 4 decimal)

Mean of sample mean = 7070

Standard deviation of sample mean = 18.3485

orchestra answered 2 years ago
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