Week 4 Conclusion: Sample Variability

Question 1

Key Concepts in Statistical Inference
Variable: ____ (e.g. ____)
____:
Statistic: ____ (e.g. __, __, __)
__:
__:
__:
Parameter: ____ (e.g. __, __, __)
__:
__:
__:

Answer 1

Key Concepts in Statistical Inference
Variable: An attribute of each unit (e.g. x, y …)
x/y = height, weight…

Statistic: An attribute of the sample (e.g., x̄, p̂, s).
x̄ (bar) = average of all xs in a sample
p̂ (hat) = sample proportion/estimated population proportion.
s = sample standard deviation.

Parameter: A attribute of the population (e.g., μ, p, σ).
μ = population mean
p = population proportion
σ = population standard deviation

Question 2

Sampling Variability
____
→ Estimates ____

Answer 2

Variations in statistics from one sample to another in the same population
→ Estimates how close the statistic is to the population parameter

Question 3

Sampling Distribution
____
→ Describes ____()

Answer 3

The distribution of a statistic’s values in all (# sample has to be huge) possible samples of the same size (SRS) from the same population.
→ Describe sampling variability/error

Question 4

Sampling distribution and increase in n (sample size)
Center:
Spread:
Shape:

Sampling variability and and increase in n (sample size)

Larger the sample size, ____ (____), ____ , ____

(Smaller the sample size is the opposite)

Answer 4

Center: stays the same

Spread: decreases as the sample size increases

Shape: both are unimodal bell shaped.

Larger the sample size, more population is represented in the sample (less likely the result is due to chance), the sample statistic will be closer to the population parameter, smaller the sampling variability.

Smaller the sample size, less population is represented in the sample (more likely the statistic is due to chance), further the sample statistic is to the population parameter, larger the sampling variability.