Week 4

When solving problems where you need the sampling distribution of r, what is the reason for converting from r to z'?

The reason for converting from r to z' is that transforming r to z' makes it normally distributed with a known standard error.

True/false: In your school, 40% of students watch TV at night. You randomly ask 5 students every day if they watch TV at night. Every day, you would find that 2 of the 5 do watch TV at night.

false

True/false: The sampling distribution of r = .8 becomes normal as N increases.

false

True/false: You choose 20 students from the population and calculate the mean of their test scores. You repeat this process 100 times and plot the distribution of the means. In this case, the sample size is 100.

false

Standard error of z'

= 1/ sqrt(N-3) N is the number of pairs of score

True/false: The median has a sampling distribution

true

Central Limit Theorem?

Given a population of any distribution with a mean (mu) and variance (sigma^2) The sampling distribution if the mean approaches a normal distribution with mean (mu) and variance (sigma^2)/N

If sample means are about the same how does that affect the standard error of the mean? what is the sample means vary greatly?

If the sample means are about the same, then the standard error of the mean is small If the sample means vary greatly then the standard error of the mean is large

In the population, the mean SAT score is 1000. Would you be more likely (or equally likely) to get a sample mean of 1200 if you randomly sampled 10 students or if you randomly sampled 30 students? Explain.

It would be more likely with a sample of 10. The sample mean tends towards the population as sample size increases.

How do you determine how different a sample statistic is likely to be from a population parameter?

Made by relative and sampling distribution of the mean, for a sample size of two. Can only be with a discrete distribution.

What formula do you use to find SD when given r?

SD = 1/sqrt(N-3)

What is the shape of the sampling distribution of r? In what way does the shape depend on the size of the population correlation?

The shape of the sampling distribution of r is skewed: if the correlation is positive then the distribution will be negatively skewed and if the correlation is negative then the distribution will be positively skewed. The shape depends on the size of the population correlation in that as the correlation increases (in either the positive or negative direction), the skew becomes more pronounced. So, the greater the absolute value of the population correlation, the more pronounced the skew.

True/false: The standard error of the mean is smaller when N = 20 than when N = 10.

True

The sampling distribution equals the relative frequency distribution when there is what?

an infinite number of samples

What does r mean?

correlation coefficient

Sampling distributions reveal how much ___________ statistics vary from ___________ parameters.

sample; population

All statistics, not just the mean, have __________ ___________.

sampling distributions

What does sigma_M mean

standard error

Fisher's z' Transformation?

z' = (.5)ln(1+r/1-r)

What formula do you use to turn r to z score?

z' = 0.5 ln[(1+r)/(1-r)]