Topic 7: Chance Variability

Question 1

The observed value is equal to…

Answer 1

Observed value = expected value + chance error

Question 2

What can the chance error be modeled as in the box model?

Answer 2

The chance error can be modeled as the standard error in the box model.

Question 3

Compare the Gambler’s Fallacy and the Law of Averages

Answer 3

• Gambler’s Fallacy: thought that as the number of tosses increases, the size of chance error will decrease which is wrong.
• Law of Averages (Law of Large Number): as the number of tosses increases, the absolute size of CE will go up but the percentage size will stabilize, then reach a relative frequency or converge to EV

Question 4

Explain the Central Limit Theorem and how it is related to histogram graph

Answer 4

When drawing random from any box with replacement, if the sample size is sufficientl large, then the distribution of the sum or mean of the sample is approximately Normal.

For repeated simulations of a chance process resulting in a sum/mean, the simulation histogram of the observed values converges to the probability histogram (Normal model).

Question 5

How is continuity correction used?

Answer 5

When we apply the box model, as the box is discrete, we can often improve the use of the Normal appriximation by slightly adjusting the thresholds.

Question 6

When using Normal model, the EV and SE are…

Answer 6

The EV is mean and the SE is standard deviation of the Normal model.

Question 7

Describe different types of histogram

Answer 7

• Data histogram: represents data by area
• Probability histogram: represents chance by area
• Simulation histogram: represents chance by area with different simulations

Question 8

In a skewed box, increasing replicates and sample size result in…

Answer 8

• Increasing sample size will make the histogram approach Normal curve.
• Increasing replicates of the sample will make the histogram approach box distribution.

Question 9

T/F
“If you toss a biased coin, there will always be chance variability. However, for a fair coin, the chance variability will be zero.”

Answer 9

False
Because there will always be a certain degree of chance error or chance variability.

Question 10

In the Box Model, which of the following does the box represent?

Answer 10

The box represents the summary of the population.

Question 11

T/F
“For repeated simulations of any chance process, the simulation histogram converges to the probability histogram.”

Answer 11

False
This only applies to repeated simulations of chance process resulting in sum or mean.

Question 12

T/F
“Taking more than 30 draws ensures that the CLT holds and the probability histogram will closely follow the Normal curve.”

Answer 12

False
Taking more than 30 draws does not ENSURE that CLT holds. Rather, it is just a minimum sample size in order to taking CLT into account.