Module 8

Question 1

What is a parameter?

Answer 1

A constant that describes a population characteristic; value may be unknown.

Question 2

What is a statistic?

Answer 2

A random variable that describes a characteristic of a sample; depends on the chosen sample.

Describes a characteristic of a sample.
A random variable, as it depends on the chosen sample.

Question 3

What is a population parameter?

Answer 3

Describes a characteristic of the population.
It is constant, but its value may be unknown.

Question 4

Sample proportion vs sample mean

Answer 4

Sample Proportion: Proportion of observations with a specific characteristic.

Formula: p=x/n

Example: Proportion of left-handed people.
Sample Mean: Average value in a sample. Example: Average annual income.

Question 5

Why use sample statistics?

Answer 5

Sample statistics are used to estimate unknown population parameters.

A single population can have many possible samples of a given size.

Question 6

Confidence interval for population mean (standard deviation known)

Answer 6

Use sample data to estimate the population mean with a certain level of confidence. Example: 90% confidence interval.

Question 7

Estimator vs estimate

Answer 7

Estimator: A rule/formula used to estimate a parameter (e.g., sample mean).

Estimate: A specific calculated value of the parameter from sample data.

Question 8

What is alpha (a)?

Answer 8

The allowed probability of error in a statistical test.

Also known as the level of significance (introduced in Chapter 9).

Question 9

Confidence coefficient vs confidence level

Answer 9

Confidence Coefficient: The proportion of confidence intervals that would contain the true parameter if repeated sampling occurred (e.g., 0.95).

Confidence Level: The percentage representation of the confidence coefficient (e.g., 95%).

Question 10

Key features of t-distribution

Answer 10

Symmetric around a mean of zero but with broader tails than the normal (Z) distribution.
The shape depends on degrees of freedom (df).
Fewer df → broader tails.
As df increases, the t-distribution approaches the Z-distribution.
Also called “Student’s t” or t-scores.

Question 11

When to use the t-distribution vs z-distribution

Answer 11

Use z-distribution when the population standard deviation (σ) is known.
Use t-distribution when σ is unknown and sample size is small.

Question 12

What factors influence confidence interval width?

Answer 12

Sample Size: Larger samples → narrower confidence intervals.

Confidence Level: Higher confidence levels (e.g., 99%) → wider intervals.

Population Variability: Greater variability → wider intervals.

Question 13

Confidence interval for population mean when standard deviation is unknown

Answer 13

Use the t-distribution instead of the z-distribution.

The formula for the confidence interval:
x±t×s/sqrt n

x bar = sample mean
t = critical t-value based on degrees of freedom (df)
s =. sample standard deviation
n = sample size

Question 14

What is the formula for degrees of freedom (df)?

Answer 14

df = n – 1