Suppose a researcher wants to learn more about the mean attention span of individuals in some...

Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20 36 . Based on the parameters given in this example, answer the following questions:

What is the population mean (μ)? : 20

What is the population variance : 6 Sketch the distribution of this population. Make sure you draw the shape of the distribution and include the mean plus and minus three standard deviations. Now say this researcher takes a sample of four individuals (n = 4) from this population to test whether the mean attention span in this population is really 20 minutes attending to some task.

I only need questions 4-7

4. What is the mean of the sampling distribution for samples of size 4 from this population? Note: The mean of the sampling distribution is .

5. What is the standard error for this sampling distribution? Note: The standard error of the sampling distribution is .

6. Based on your calculations for the mean and standard error, sketch the sampling distribution of the mean taken from this population. Make sure you draw the shape of the distribution and include the mean plus and minus three standard errors.

7. If a researcher takes one sample of size 4 (n = 4) from this population, what is the probability that he or she computes a sample mean of at least 23 (M = 23) minutes? Note: You must compute the z-transformation for sampling distributions, and then refer to the unit normal table to find the answer.

Solutions

Expert Solution

4. What is the mean of the sampling distribution for samples of size 4 from this population? Note: The mean of the sampling distribution is
mean = 20
The mean of the sample draw from the population will have the same mean.

5. What is the standard error for this sampling distribution? Note: The standard error of the sampling distribution is .
Variance = 36
Standard deviation = 6

standard error for this sampling distribution

orchestra answered 1 year ago

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