Lecture 10: Hypothesis Testing

Question 1

Probability

Answer 1

the relative likelihood of an event occurring

Question 2

probability is measured on

Answer 2

a scale from 0 (absolute certainty the event will not occur) to 1 (absolute certainty the event will occur
*sometimes discussed in terms of a %

Question 3

normal probability distribution

Answer 3

a density function which assumes a bell-shaped curve

Question 4

significance

Answer 4

• many random variables observed in nature have a frequency that follows a bell shape.
• provides a large sample approximation to the probability distributions for many estimators and test statistics.

Question 5

significance allows us

Answer 5

to make inferences about the population from which our samples are drawn

Question 6

Central Limit Theorem

Answer 6

in random samples of N, observations drawn from a population with a mean (u), SD (sigma), the samples means will be approx. normally distributed with a mean equal to U and a SD = sigma/SQRT(N) (SEM)

Question 7

similarities between t-distribution curve and normal distribution

Answer 7

t-distribution - family of curves.

-both mound-shaped and symmetrical

Question 8

difference between t-distribution and normal distribution curve

Answer 8

t-distribution changes shape as a function of the sample size - the “tails” become thicker as N decreases

Question 9

confidence interval

Answer 9

constructed around our point estimate of the population mean.
- consists of a lower confidence bound and an upper confidence bound with the population mean contained within this interval (1-alpha) percent of the time

Question 10

sample mean

Answer 10

an unbiased estimator for the population mean

*this estimate, by itself, gives us no idea of its accuracy

Question 11

research hypothesis

Answer 11

a prediction based on the theory being tested; on preliminary observations; on contentions or guesses.

a language-based statement of what we are trying to prove

Question 12

research hypothesis example

Answer 12

gender affects intelligence eye roll

Question 13

Null hypothesis

Answer 13

a mathematical statement, usually in population parameters, of no difference
-can be expressed as a function of the parameters equaling zero, hence term “null”

Question 14

null hypothesis example

Answer 14

u(men) - u (female) = 0

u(men) = u(female)

Question 15

alternative hypothesis

Answer 15

an objective mathematical statement of the research hypothesis similar to the null hypothesis
- we PROVE the alternative hypothesis by showing that the null is unlikely to be true

Question 16

alternative hypothesis example

Answer 16

u(male) - u(female) does not = 0