Assignment #2 - cat by cat

Question 1

which law says the result obtained
from a large number of trials should be close to the expected result, and will tend
to get closer to the expected result as more trials
are performed.

Answer 1

law of large numbers

Question 2

if individual
outcomes are uncertain (up to chance) but there is
nonetheless a regular distribution of outcomes in
a large number of trials, what do we call it?

Answer 2

A random phenomenon

Question 3

the proportion of times the
outcome would occur in an indefinitely long
series of trials of a random phenomenon

Answer 3

Probability

Question 4

mathematical

descriptions of long run regularity of random phenomenon

Answer 4

Probability models

Question 5

What does a probability model consist of? (3)

Answer 5

1 - Sample space (s)
2 - Event
3 - Probability of each event

Question 6

The set of all possible outcomes in a random phenomenon

Answer 6

Sample space (s)

Question 7

The probability model for a random phenomenon

with a FINITE number of possible outcomes

Answer 7

discrete probability model

Question 8

How do you describe a discrete probability model

Answer 8

list the possible outcomes and

their associated probabilities.

Question 9

How do you describe a discrete probability model

Answer 9

list the possible outcomes and

their associated probabilities.

Question 10

What is the probability model of a coin toss

Answer 10

S = {Heads (0.5), Tails (0.5)}

Question 11

In a probability model, what does the value in brackets ( ) represent

Answer 11

the probability of that event

Question 12

The probability model for a random phenomenon

with an infinite number of possible outcomes

Answer 12

Continuous probability model

Question 13

How do you express a continuous probability model?

Answer 13

a continuous curve with the total area under the

curve equal to 1, X-axis = possible outcomes

Question 14

What is a continuous curve + axis combo for a continuous probability model called?

Answer 14

Probability distribution

Question 15

probability distribution obtained through a large number of samples drawn from the population.

Answer 15

Sampling distribution

Question 16

the sampling distribution for p has known

characteristics if the sample size is large enough

Answer 16

Central Limit Theorem

Question 17

systematic bias that arises from using

nonprobability sampling methods.

Answer 17

Sampling methods

Question 18

he error that occurs when using a
statistic based on a sample to predict the value of a
population parameter.

Answer 18

Sampling error

Question 19

the probability distribution that specifies probabilities for the possible values a statistic can take.

Answer 19

The sampling distribution

Question 20

the standard deviation of the sampling

distribution.

Answer 20

Standard error

Question 21

a range of values which is
computed from sample data and might contain
the unknown population parameter.

Answer 21

Confidence interval

Question 22

Two components of a confidence interval

Answer 22

1. interval

2. Confidence level C

Question 23

what is the interval component of a confidence interval

Answer 23

calculated from the data, usually in the

form ‘estimate ± margin of error.’

Question 24

What is the confidence level C portion of a confidence interval

Answer 24

our level of
confidence that the interval includes the population
parameter.

Question 25

What is the most common confidence interval

Answer 25

95%

Question 26

How do you narrow a confidence interval

Answer 26

Make C smaller, e.g., using C = 90% instead of C = 95% OR make N larger

Question 27

Why would you want to narrow a confidence interval?

Answer 27

to produce a smaller margin of error.

Question 28

Do confidence intervals utilize sample size (n) or population (N)?

Answer 28

sample size (n)

Question 29

6 Elements of a test of significance

Answer 29

1. null and alternative hypotheses 2. test statistic 3. p-value 4. alpha-level 5. conclusion 6. assumptions that must be met

Question 30

a statement about some characteristic of a variable or a collection of variables.

Answer 30

Hypothesis

Question 31

Does a hypothesis pertain to the characteristics of a population or a sample?

Answer 31

Population

Question 32

What does a significance test include?

Answer 32

two specific hypotheses pertaining to the value of a given parameter.

Question 33

the hypothesis that is directly tested. the parameter in question has a value corresponding to ‘no effect’ or ‘no association.’

Answer 33

null hypothesis (Ho)

Question 34

a hypothesis that directly contradicts the null hypothesis. the parameter in question falls in some alternative set of values to that specified by the null hypothesis.

Answer 34

alternative hypothesis (Ha)

Question 35

In a test of significance, which hypothesis do we assume is true?

Answer 35

Null hypothesis (Ho)

Question 36

What does a test of significance analyze?

Answer 36

Strength of evidence AGAINST the null hypothesis

Question 37

Does proving insufficient evidence against Ho mean Ho is true?

Answer 37

No, it just means that we don't have enough proof that its not true

Question 38

a statistic calculated from the sample data to test the null hypothesis.

Answer 38

A test statistic.

Question 39

the probability, when Ho is true, of producing a test statistic value that is at least as contradictory to Ho as the value actually observed.

Answer 39

The p-value

Question 40

The smaller the p-value in a test statistic, what does this mean?

Answer 40

The more strongly the data contradicts Ho.

Question 41

a number such that one rejects Ho if the p-value is less than it

Answer 41

α-level (alpha-level)

Question 42

What is another term for the a-level

Answer 42

he significance level of the test.

Question 43

What are the most common a-level values for significance levels of test statistics

Answer 43

0.05 and 0.01.

Question 44

What do we do if p < alpha (e.g., p < 0.05) ?

Answer 44

We reject Ho and | accept Ha.

Question 45

What do we do if p > alpha (e.g., p > 0.05)

Answer 45

we do not reject Ho and therefore do not accept Ha.

Question 46

Assumptions of a significance test

Answer 46

1. Randomization 2. Type of variable(s) matches the type of test (quantitative, categorical, etc.) 3. Shape of the distribution of a variable in the population (sometimes MUST be normal) 4. Sample size (some tests have minimum)

Question 47

Why would decisions in tests of hypotheses always have some uncertainty?

Answer 47

Sampling error

Question 48

Sampling error when Ho is rejected even though it is actually true.

Answer 48

Type I error (or false positive)

Question 49

Sampling error when Ho is not rejected even though it is actually false.

Answer 49

Type II error (or false negative)

Question 50

For bivariate associations, visually displays the number of observations observed at all the combinations of possible outcomes for the two variables.

Answer 50

A contingency table

Question 51

In a contingency table, the row totals considered together and the column totals considered together

Answer 51

Marginal distributions

Question 52

What are the marginal distributions of a contingency table?

Answer 52

The frequency distributions of the two variables.

Question 53

percentage of the | row total that pertains to each column.

Answer 53

Row percentages

Question 54

the percentage of the column total that pertains to | each row

Answer 54

Column percentages

Question 55

If there is an independent and dependent variable, which percentage is included?

Answer 55

The percentage of the location of the independent variable (i.e., if in rows, use row percentage).

Question 56

a measure of the strength of an association between two categorical variables.

Answer 56

Cramer's V

Question 57

What is the range of Cramer's V?

Answer 57

0 (no association) to 1 (perfect association).

Question 58

A measure of the strength of association between two ordinal categorical variables

Answer 58

Kendall's tau-b

Question 59

Range of kendall's tau b

Answer 59

low of –1 (a perfect negative association) through 0 (no association) to a high of 1 (a perfect positive association)

Question 60

The Chi-squared test of significance is used to help produce what?

Answer 60

Cramer's V

Question 61

What are the hypotheses of the Chi-squared test of significance?

Answer 61

- Ho: X and Y are unassociated in the population | - Ha: X and Y are associated in the population

Question 62

How do we know, looking at a contingency table, if two variables are unassociated in the population?

Answer 62

The percentages in the contingency table between the two variables in the population are the same.

Question 63

What counts is the Chi-squared test of significance based upon?

Answer 63

Observed counts vs expected counts.

Question 64

The count for a cell in the contingency table between X and Y is the number of observations in the sample that fall in that particular cell.

Answer 64

Observed count

Question 65

What does the expected count of a bivariate association equal?

Answer 65

the product of its row total and its column total divided by the total sample size.

Question 66

assesses the magnitude (sum) of the differences between the observed and expected counts.

Answer 66

The Chi-squared test statistic

Question 67

What does the area under the curve to the right of the Chi-squared test statistic calculated for our sample represent?

Answer 67

probability of finding a test statistic | as or more contradictory to the null hypothesis as this one, just by chance, when the null hypothesis is true.

Question 68

Data assumptions for Chi-squared test of significance (3)

Answer 68

1. No more than 20% of the expected counts are less than 5 2. all individual expected counts are 1 or greater. 3. ll four expected counts in a 2 x 2 table should be five or greater.

Question 69

Does a small p-value always = strong association?

Answer 69

No, big difference between statistical | significance and practical significance.

Question 70

What are the hypotheses for the test of significance for Kendall's tau b

Answer 70

Ho: tau-b = 0 in the population Ha: tau-b is not equal to 0 in the population.

Question 71

Which test of significance is more discriminating?

Answer 71

The test of significance for Kendall's tau-b?