A population of 32 scores has a rectangular shape and a can of mu = 44. If all p

Question

A population of 32 scores has a rectangular shape and a can of mu = 44. If all possible samples are taken from this distribution of scores, how what will the shape of the distribution of sample means be? If all possible samples are taken from this distribution of scores, what will the mean of the sampling distribution be? Describe what the standard error of the mean (sigma_M) represents? For a population with a mean of mu = 50 and a standard deviation of sigma =10, how much error, on average, would you expect between the sample mean (M) and the population mean for: A sample of n = 4 scores A sample of n = 16 scores A sample of n = 25 score A random sample of n = 30 scores is selected from a normal population with a mean of mu = 90 and a standard deviation of sigma = 12 What is the probability that the sample mean is between M = 89 and M = 93? What is the probability that the sample mean is between M = 84 and M = 85 What is the total probability that the sample mean is either below M = 86 or above M = 92?

Explanation / Answer

12a:

since sample size=n=32,n>30

according to central limit theorem

sample size follows normal distribution

12b:

sample mean of the sampling distribution is

mean=44

Solution13:

standard error of the mean=std deviation/sqrt(sample size)

variabaility of distribution of sample means is measured by the standard deviation of the sample means

and is called standard error of the mean.

Solution14:

14a)

SE=50/sqrt(4)=50/2=25

14(b)

SE=50/sqrt(16)=50/4=12.5

14(c)

SE=50/sqrt(25)=50/5=10

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