Quiz 13.1

Which combination of factors will produce the smallest value for the standard error?​

A large sample size and small population standard error will lead to small standard error. Refer to the formula of the standard error to see why this is the case.

What happens to the standard error of M as sample size increases?​

Error decreases as sample size increases

For a particular population, a sample of n = 9 scores has a standard error of 8. For the same population, a sample of n = 16 scores would have a standard error of ____.​

First, you will need to find the standard deviation: Transform the formula: σM = σ/√n σ = σM * √n = 8 * 3 = 24 Now use that same standard deviation (24) to find the new standard error: σM = σ/√n = 24/4 = 6 GW pg 202-203

For a normal population with a mean of µ = 80 and a standard deviation of σ = 10, what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?​

First, you will need to find the standard error: σM = σ/√n = 10/√25 = 2 Then apply the z-score formula: Z = (M-µ)/ σM = (=75-80)/2 = -2.5 You know that the z-score is to the left of the mean because it is negative. You want the probability of a sample mean greater than z=-2.5. Therefore, look for the 2.5 in the "proportion in the body" column. P=0.9938 GW pg 207-208

A random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10. If the sample mean is M = 90, what is the z-score for the sample mean?​

First, you will need to find the standard error: σM = σ/√n = 10/√4 = 5 Then apply the z-score formula: Z = (M-µ)/ σM = (90-80)/5 = 2 GW pg 207-208

What happens to the expected value of M as sample size increases?​

Sample size does not affect the expected value of mean

If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means? ​

The average of all sample means is the same as the expected value of the mean, which always equals the population mean

If random samples, each with n = 9 scores, are selected from a normal population with µ = 80 and σ = 36, then what is the expected value of the mean of the distribution of sample means?​

The expected value of the mean always equals the population mean

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the expected value of M, the mean of the distribution of sample means?​

The expected value of the mean always equals the population mean

A sample obtained from a population with σ = 12 has a standard error of 2 points. How many scores are in the sample?​

Transform the formula: σM = σ/√n n = (σ / σM)2 = (12/2)2 = 36 GW pg 202-203