mtehts

Question 1

Critical Region

Answer 1

A critical region is the range of values of the test statistic that would lead us to reject 𝐻0. The threshold value between the critical region and acceptance region is the critical value.

Question 2

How will a distribution change when the intervals change?

Answer 2

We don’t know the distribution of the test statistic within the interval.

Question 3

Type I Error

Answer 3

Concluding that there is evidence for rejecting the null hypothesis, when in reality the null hypothesis is true.

Probability is the probability of rejecting the null hypothesis. (Significance level/s)

Question 4

Type II Error

Answer 4

Concluding that there is evidence to not reject the null hypothesis, when in reality the null hypothesis is false.

Probability of accepting the null hypothesis with the true probability (Probability of the acceptance region w/ true probability)

Question 5

Sampling Types

Answer 5

Systematic Sampling
Selecting sampling units from a population at a fixed periodic interval.
- Bias-free
- Requires a sampling frame
- May lead to inaccuracies if population size is unknown

Simple Random Sampling
Selecting sampling units randomly, each unit has an equal chance of being selected.
- Bias-free
- Requires a sampling frame
- Is unspecific; can be used on any dataset with no other steps or special knowledge required.

Opportunity Sampling
Selecting sampling units based on what is accessible and convenient at the time and place the investigation is taking place.
- Very simple to carry out, inexpensive
- Subject to selection bias will make results not accurate

Question 6

Sampling Frame

Answer 6

Indexed list of all sampling units in a population that is being tested.

Question 7

Significance Level

Answer 7

The threshold value between the acceptance and critical regions (p-value of test statistic less than or equal to the significance level leads to the conclusion that there is evidence for rejecting the null hypothesis)

Question 8

Probability Distributions & Conditions for each

Answer 8

Binomial:
Each event is independent and has constant probability.
Each event has only two outcomes, success or failure.
There is a fixed number of trials.

Poisson:
There is a constant average rate that the events occur at.
Events don’t occur simultaneously.
Each event is independent.

Discrete Uniform:
Each outcome has equal probability. (e.g dice roll or choosing numbered cards)

Question 9

Skewness

Answer 9

Positive skew:
Bulk of test statistics are nearer 0, distribution tails away from 0.
(mean > median > mode)

Negative skew:
Bulk of test statistics are further from 0, distribution tails towards 0.
(mode > median > mean)

Question 10

Correlation Terms

Answer 10

Strong positive
Weak positive

Strong negative
Weak negative

Zero correlation

Question 11

Measures of Central Tendency

Answer 11

Mean
Median
Mode

Question 12

Measures of Variability

Answer 12

Range
Interquartile Range
Standard Deviation
Variance

Question 13

Standard Deviation Equations

Answer 13

For discrete test statistics:
σ² = Σ( (x-x̅)² ) / N

For frequency distributions:
σ² = ( (Σfx²) / (Σf) ) - x̅²

Question 14

P-Value

Answer 14

Probability of obtaining a test result based on the test’s binomial model under the assumption of the null hypothesis being true.

Question 15

Interpreting Regression Line Equation

Answer 15

Gradient: As X increases by 1, Y increases by m 𝐨𝐧 𝐚𝐯𝐞𝐫𝐚𝐠𝐞.

Intercept: When X is 0, Y is C

Question 16

Mechanics

Answer 16

really easy