Week 3

Question 1

What is Chebyshevs theorem?

Answer 1

For any set of observations, the proportion of values that lie within k standard deviations of the mean is at least:

1-(1/k^2) given k>1

Question 2

What does sd measure?

Answer 2

Dispersion with respect to mean

Question 3

What is a probability?

Answer 3

A value between 1 and 0 describing relative possibility of an event occurring

Question 4

What is a random variable?

Answer 4

Quantity resulting from an experiment that can assume different values

Question 5

What is a probability distribution?

Answer 5

Shows all possible outcomes of a test and the probabilities associated to each outcome

Question 6

6 characteristics of a normal distribution?

Answer 6

Bell shaped
Area under curve = 1
Asymptotic to X axis
Symmetrical about the mean
Mean=median=mode
Peak in centre

Question 7

2 measures of distributions?

Answer 7

Skewness

Kurtosis

Question 8

What is Kurtosis?

Answer 8

How peaked it is (normal dist. = 3)

Question 9

What is leptokurtic Kurtosis?

Answer 9

Kurtosis >3

Question 10

What is platykurtic Kurtosis?

Answer 10

Kurtosis <3

Question 11

Kurtosis equation?

Answer 11

Kurtosis = (Σ(Xi-μ)^4)/((Σ(Xi-μ)^2)^2)

Question 12

What is a standard normal probability distribution?

Answer 12

Mean = 0
Sd = 1

Question 13

What does the z-score tell us?

Answer 13

The number of sd’s a score lies above or below the mean

Question 14

What is a probability sample?

Answer 14

Each item in sample has a known probability of being included in the sample

Question 15

4 ways to produce a probability sample?

Answer 15

1) simple random sampling
2) systematic random sampling
3) stratified random sampling
4) cluster sampling

Question 16

What is cluster sampling?

Answer 16

Population is divided into primary units (clusters), individual clusters are randomly selected then a random sample is taken from each selected cluster

Question 17

What is sampling error?

Answer 17

The difference between sample statistic and its corresponding population parameter

Question 18

What is a sampling distribution?

Answer 18

Probability distribution of a statistic for all possible samples of a certain size N

Question 19

What is empirical sampling distribution?

Answer 19

Take the whole population, split into many samples of equal size and look at distribution formed

Question 20

Characteristics of empirical sampling distribution? (3)

Answer 20

Mean pop = mean of distribution of sample means
Spread of pop>spread of dist. of sample means
Dist. Sample means is similar/can be approximated by normal distribution

Question 21

Standard deviation of a sample = ?

Answer 21

σ/(N)^0.5

Question 22

What is the central limit theorem?

Answer 22

Sampling distribution of the mean of any independent random variable will be normal or nearly normal

Question 23

When is an estimator of the mean unbiased?

Answer 23

When μ (sample) = μ (population)

Question 24

What is bias proportional to?

Answer 24

Error

Question 25

What determines if a sampling distribution is efficient?

Answer 25

If σ is small it is efficient

Increasing N increases efficiency