Week 5 day 1

Question 1

What would a ‘frequentist’ say probability is?

Answer 1

Proabability is based on long-run frequency of events.
Probability is objective.
Only applies to repeatable events.

I don’t fully get this.

Question 2

What would a ‘Baysianist’ say probability is?

Answer 2

Probability is a degree of belief.
Probability is subjective and is in the beliefs of rational agents.
Can apply to anthing you believe in.

What does an indealised, rational agent belief will happen?

I don’t really get this.

Question 3

What is the difference between binomial and normal distributions?

Answer 3

A binomial distribution represents the probability distribution of count data where there are two possibilities of each event.

Question 4

Can a normal distribution be described fully with the mean and standard deviation?

Answer 4

Yes.

Question 5

Are the mean and standard deviation we calculate from our samples esimates of population parameters?

Answer 5

Yes.

Question 6

The sample mean is an estimator of the population mean.

What makes a good ‘estimator’?

Answer 6

Unbiased.
Consistent.
Low variance.

The mean is a pretty good estimator.

Question 7

Do we ever know the true population mean?

Answer 7

No.
We use estimates from samples from the world.

Question 8

Is the estimated population mean an inferential statistic?
Is the sample mean an inferential statistic?

Answer 8

Yes.

No. It is a description of our data.

Question 9

What is the sampling distribution of the mean?

Answer 9

Distribution of means from a sample of samples.

Question 10

Do larger sample sizes decrease our error on our estimation of the true mean?

Answer 10

Yes. With lager sample sizes we decrease the standard error of the mean.
Standard error of the mean = standard deviation of the population/square root of the sample size.

Question 11

Why does it not matter that we do not know the true population mean?

How are we able to estimate the true population mean without having to measure the whole population?

Answer 11

By plotting the means of multiple samples drawn from the population we create the sampling distribution of the mean. The centre or mean of the this distribution is our best estimate of the true population mean. It is a good estimate, especially the more samples from the population we have.

Andy says this is the miracle of statistics.
Even with one experiment, we can estimate our population mean and determine how certain/uncertain we are of this estimate.