Chapter 11 - Statistics

Question 1

What are the three types of studies? (3)

Answer 1

1. Observational Studies
2. Surveys
3. Experimental Studies

Question 2

Definition of Observational Studies (4)

Answer 2

• Researchers observe/measure subjects (“observe” “record” “collect data”)
• NO interference, NO manipulation to avoid bias
• Must be chosen from a random sample
• Cannot show cause & effect with NO groups

Question 3

Definition of Surveys (4)

Answer 3

• ASKS people questions to collect self-reported responses (no observation/treatments)
• Must be chosen from a random sample
• Cannot show cause & effect with NO groups
• KEY WORD: ASKED

Question 4

Definition of Experimental Studies (3)

Answer 4

• Researchers CHANGE a variable and subjects are randomly assigned to groups
• Control: No Treatment, Treatment: Receives Changed Variable
• Designed to show cause and effect

Question 5

What methods are used to observe a population? (3)

Answer 5

• Sample: Smaller group selected from population measured to represent whole population
• Random Sample: Used in OBSERVATIONAL STUDIES, Avoids Bias, Flip Coin/Generators/Tables
• Random Assignment: Used in EXPIREMENTAL STUDIES, Divides Subjects into Groups (Flip Coin/Generators/Tables)

Question 6

Definition of Explanatory Variable
Definition of Response Variable

Answer 6

• Independent Variable: CHANGED, IMPOSED, or thought to CAUSE an effect
• Dependent Variable: MEASURED to see the effect of the explanatory variable

Question 7

Definition of Random Digits Table (2/5)

Answer 7

Definitions:
- Long string of digits randomly generated
- This randomizes numbers to select people fairly (in random sampling/assignment) to keep studies unbiased
How to Use:
- Assign each person in the population a number from 1 up to the
population size
- Must use correct number of digits based on population size (Ex: If population size is 78, you must use TWO digits, if population is 300, you must use THREE digits)
- Read the random digits in groups matching the number of digits
you assigned to select individuals’ numbers (2‑digit groups, 3‑digit groups)
- Skip any number that does NOT correspond to a real person
(outside the interval) and ignore repeats
- Must end up with unique selected individuals for your sample/group that fit between the intervals

Question 8

Definition of Random Number Generator (6)

Answer 8

• Take a random sample from a population using a calculator to avoid bias
• Calculator generates random integers between 1 and population size
• Each integer corresponds to one person in the population
• If a number repeats, ignore it
• If more than 10 numbers are generated, keep first 10 UNIQUE valid numbers
• Look up the data for each selected person and calculate sample mean/proportion if they ask you to

Question 9

Definition of a Statistics (and how can be used) (5)

Answer 9

• Summary number of a SAMPLE, such as sample mean (x̄)
  or sample proportion (p̂)
• Sample Mean (x̄): average of sample’s quantitative data
• Sample Proportion (p̂): proportion of sample with a certain trait
• Creates a Statistical Inference: Sample statistics draw conclusions about population parameters
• Random samples give unbiased results, so sample means/proportions tend to be close to true population mean/proportion

Question 10

Definition of Parameter (4)

Answer 10

• Summary number (mean/proportion) that describes an ENTIRE POPULATION
• TRUE value that describes an entire population
• Cannot actually calculate parameter in practice since populations are usually too large to measure completely
• Statistic from a random sample is used to ESTIMATE the parameter, and a good statistic (if from randomized sample) will be close to the true value

Question 11

Definition of Sampling Distribution (4)

Answer 11

• Distribution when you take MANY random samples from the same population and record a statistic from each sample (sample mean or sample proportion)
• When you plot all those statistics (like dots on a dot plot), you can see the overall spread and shape of the curve across repeated samples
• Each sample produces a slightly different statistic because every sample is different (sample variability)
• When MORE samples are taken, the center of the sampling distribution (mean if symmetric, median if skewed) tends to be very close to the TRUE population parameter and has a smaller standard deviation/variability

Question 12

When taking sample distribution, what is true when more samples are taken? (2)

Answer 12

• Center (mean if symmetric, median if skewed) tends to be the closest to the TRUE population parameter
• Distribution/Curve has a smaller standard deviation/variability

Question 13

Definition of Confidence Interval (and how to find approximate + actual) (1/3/2)

Answer 13

Definition: Range of values that is 95% of distribution that show a reasonable expectation a sample statistic (like a sample proportion) to be
How to find approximate:
- Remove most extreme 5% of dots (unusual/outliers) from far L/R
- Choose final dot that keeps data most symmetric/centered around mean when choosing b/w L or R
- Lowest remaining dot and highest remaining dot form interval
How to find actual:
- Provided Mean and Standard Deviation (Mean ± 2SD)
- Find margin of error (Mean ± ME)
- NOTE: Use Interval Notation

Question 14

Definition of the Margin of Error

Answer 14

Definition:
- Natural wiggle room showing how far a sample result might be from the true population value due to random chance not actual error
- Half the distance b/w confidence interval OR distance b/w one end of the confidence interval and the center (true population value)
How to Calculate:
- (Highest Reasonable Value − Lowest Reasonable Value)/2
- 2 x SD (b/c whole 95% interval is 4 × SD since 2 SD covers the distance up from the mean and 2 SD covers the distance down)