AP Final

Question 1

Inference for Proportions (Conditions)

Answer 1

Random: Data from a random sample(s) or randomized experiment

Normal: At least 10 successes/failures (in both groups, for a two sample problem)

Independent: Independent observations and independent samples/groups; 10% condition if sampling without replacement

Question 2

Interpret ‘r-squared’

Answer 2

___ % of the variation in y (context) is accounted for by the least squares regression line of y (context) on x (context)

Question 3

Inference for Means (Conditions)

Answer 3

Random: Data from a random sample(s) or randomized experiment

Normal: Population distribution is normal or large (greater than/equal to 30)

Question 4

Two Sample t-test (Conclusion)

Answer 4

Fail to reject/reject the null hypothesis (state). We do/do not have enough evidence at the 0.05 level to conclude that the difference between the mean ____ for all ___ and the mean ___ for all ___ is ___.

Question 5

Chi-Square Tests (df and Expected Counts)

Answer 5

1. Goodness of Fit: df = # of categories - 1
   Expected Counts: Sample size times hypothesized proportion in each category
2. Homogeneity: df = (#rows-1)(#columns-1)
   Expected Counts: (row total)(column total)/table total

Question 6

What is Goodness of Fit Chi-Square Test used for?

Answer 6

Use to test the distribution of one group or sample as compared to a hypothesized distribution

Question 7

What is a Homogeneity Chi-Square Test used for?

Answer 7

Use when you have a sample from 2 or more independent population or 2 or more groups in an experiment. Each individual must be classified based upon a single categorical variable.

Question 8

What is an Association/Independence Chi-Square Test used for?

Answer 8

Use when you have a single sample from a single population. Individuals in the sample are classified by two categorical variables.

Question 9

Factors that Affect Power

Answer 9

1. Sample size: To increase power, increase sample size
2. Increase alpha: A 5% test of significance will have a greater chance of rejecting the null than 1% test.
3. Consider an alternative that is garter away from mu naught: Values of mu that are in mu alternative, but lie close to the hypothesized value are harder to detect than values of mu that are far away from mu naught.

Question 10

Type 1 Error

Answer 10

Rejecting mu naught when mu naught is actually true

Question 11

Type 2 Error

Answer 11

Failing to reject mu naught when mu naught should be rejected

Question 12

What is power?

Answer 12

The probability of rejecting mu naught when mu naught should be rejected (rejecting correctly).

Question 13

Inference for Regression (Conditions)

Answer 13

L-I-N-E-R

Linear: The relationship between the variables is linear

Independent: Observations, 10% condition if sampling without replacement

Normal: Responses vary normally around the regression line for all x-values

Equal Variance around regression line for all x-values

Random: Data from a random sample or randomized experiment

Question 14

Chi-Square Tests (Conditions)

Answer 14

Random: Data from a random sample(s) or randomized experiment

Large Sample Size: All expected counts are at least 5

Independent: Independent observations and independent sample/groups; 10% condition if sampling without replacement

Question 15

Can we generalize results to the population of interest?

Answer 15

Yes, if a large random sample was taken from the sample population we hope to draw conclusions about.

Question 16

Explain a P-value

Answer 16

Assuming that the null is true (context) the P-value measures the chance of observing a statistic (or difference in statistics) (context) as large as or larger than the one actually observed.

Question 17

Interpreting a Confidence Level

Answer 17

Intervals produced with this method will capture the true population ____ in about 95% of all possible samples of this same size from this same population.

Question 18

Interpreting a Confidence Interval

Answer 18

We are __% confident that the interval from ___ to ___ captures the true ______.