Confidence Intervals and Hypothesis Testing

Question 1

Margin of error

Answer 1

Measures how accurate the point estimate is likely to be in estimating a parameter
Equal to t or z times standard deviation/standard error

Question 2

How level of confidence and population size affect confidence intervals

Answer 2

Higher level of confidence: wider interval

Higher population: smaller interval

Question 3

What test statistics (such as t) measure

Answer 3

How far sample statistic is from the null hypothesis parameter

Question 4

How t distribution differs from z distribution

Answer 4

Bell shaped distribution (like z), but with slightly thicker tails
As degrees of freedom increase, t curve approaches z curve
Depends on degrees of freedom (equal to n-1)

Question 5

Robust

Answer 5

Statistical method that performs adequately even when the assumptions it is based on (such as normally distributed data) is modestly violated
Confidence interval using t distribution fits this

Question 6

What null hypothesis refers to

Answer 6

Finding of interest in sample is result of randomness

Parameter takes a particular value (p0 is equal to or less than/greater than or equal to)

Question 7

Hypothesis testing procedure

Answer 7

1. Choose a test
2. Check assumptions for chosen test (randomization, sample size, shape of population distribution)
3. Formulate hypotheses (H0 and Ha)
4. Calculate test statistic
5. Look up p value
6. Reach conclusion and state it in plain English

Question 8

What p value is likelihood of

Answer 8

Likelihood of obtaining a sample proportion or mean as extreme or more extreme given that the null hypothesis is true

Question 9

How to interpret p value

Answer 9

p is less than # (one-tailed): table value
p is greater than # (one tailed): 1-table value
p equals # (two tailed): 1-table value, then multiply by 2

Question 10

Assumptions of z test

Answer 10

Categorical data
Data obtained using randomization
Expected number of successes and failures are both at least 15
Binary (one of 2 choices)
One variable

Question 11

Assumptions of t test

Answer 11

Numerical data
Data obtained using randomization
Population distribution is approximately normal
One variable

Question 12

Assumptions of chi square goodness of fit test

Answer 12

Categorical data
More than 2 categories
One variable

Question 13

Two tail hypotheses

Answer 13

Null: mu equals m0
Alternative: mu doesn’t equal mu0

Question 14

Right tail hypotheses

Answer 14

Null: mu is less than or equal to mu0
Alternative: mu is larger than mu0

Question 15

Left tail hypotheses

Answer 15

Null: mu is greater than or equal to mu0
Alternative: mu is less than mu0

Question 16

Type I error

Answer 16

False positive: sample comes from tails
Incorrectly reject null
Decreasing alpha decreases these

Question 17

Type II error

Answer 17

Miss: underpowered study (too small of sample or too subtle of effect)
Incorrectly fail to reject null
Increasing alpha decreases these