1. Match the parameter to the item that best describes it.

x₀

(gamma)

(mu)

(sigma)

y₀

A.the point with the maximum value in a Cauchy pdf

B.Help, I don't match anyone else and I'm lonely!

C.the point with the maximum value in a Gaussian pdf

D.determines the width of the peak in a Gaussian pdf

E.determines the width of the peak in a Cauchy pdf

1. Select all of the examples which illustrate the Law of Large Numbers.

• The more times you flip a coin, the closer the ratio of heads to tails gets to 1/1.
• The larger the true mean of a distribution is, the more likely that the mean of a sample from that distribution will be close to the true mean.
• If you roll a 6 on a die, the next roll will be a 1 to even out the distribution.
• The mean of a height measurement from 63% of a group is more likely to be near the true mean height of the group than the mean of a height measurement from 39% of the group.
• The more trials in an experiment, the more likely you are to reject the null hypothesis.

1. Student's t distribution with 1 degree of freedom is identical to the normal distribution.

• True
• False

1. Student's t distribution with a large number of degrees of freedom becomes very similar to a Cauchy distribution.

• true
• false

1. Select all of the statements that are true of the Cauchy distribution.

• It can be made identical to a normal distribution by adjusting the parameters.
• A large number of samples from a Cauchy distribution will give a better estimate of its true mean.
• The tails of the Cauchy pdf are uniform past +/- gamma from x_0.
• The total area under the curve for the Cauchy pdf is always 1.0.
• The Cauchy pdf is not symmetric.

1. A lab is conducting a study using electrodes to record from the prefrontalcortex (PFC) and the lateral entorhinalcortex (LEC) in order to see if the LEC activity is more strongly influenced than the PFC activity by the location of the subject rat in a maze

Select the item which is most likely thenull hypothesisfor this study.

• The PFC activity will be more strongly correlated with location than the LEC activity will be.
• The LEC activity will be more strongly correlated with location than the PFC activity will be.
• Location will have a stronger influence on neural activity than any other environmental factor.
• The LEC activity and PFC activityhave statistically indistinguishable correlations to location in the maze.
• The location in the maze will have no influence on neural activity in the hippocampus.

1. Select the most appropriate justification for calculating the standard error of the mean (s.e.m.)from asingle sample(rather than calculating the standard deviation ofmeans from several samples)from a given population.

• A Cauchy distribution pdfis close enough to a normal distribution pdfthat we can just assume the Cauchy is normal.
• If the sample is large enough,the s.e.m.will be small enough to ignore the difference in underlying distributions.
• The means from several samples of a Cauchy distribution also make up a Cauchy distribution so taking too many samples will prevent the s.e.m.from converging.
• Even if a distribution is not normal,the means from sufficiently large samples from that distribution are normal,given the population PDF is not pathological,which is the case for a population with finite size.
• Student's t distribution can approximate both the Cauchy and normal distributions,so the method to calculate the s.e.m.is the same.