AP Statistics Inference Procedures

Probability

100

You have a bag with 5 red marbles, 3 blue marbles, and 2 green marbles. You reach in and pull out two marbles, one after the other, without putting the first one back.
What is the probability that both marbles you pull out are blue?

0.06667   OR   1/15

200

In a small classroom, there are 10 students.  6 students are wearing blue shirts.  4 students are wearing hats. 2 students are wearing both a blue shirt and a hat.
If you pick one student at random, what is the probability that they are wearing a blue shirt or a hat?

0.8

300

P(liking apples) = 0.6

P(liking apples and oranges) = 0.3

What is the probability that a person likes oranges, given that they already like apples?

0.5

400

A tech factory uses two machines, A and B, to produce microchips. Machine A produces 60% of the chips, and Machine B produces 40%. The probability that a chip from Machine A is defective is 5%. The probability that a chip from Machine B is defective is 10%. A "critical failure" occurs if a chip is defective and fails a secondary stress test. Given that a chip is defective, the probability it fails the stress test is 80% for Machine A and 60% for Machine B.

What is the probability that a randomly selected chip is either from Machine B or it is a "critical failure"?

0.424

500

In a specialized academy, students take exams in Math (m), Physics (p), and Chemistry (c). The following probabilities are known:

P(m) = 0.7       P(p) = 0.6       P(c) = 0.5

The probability of passing both Math and Physics is 0.4.  The probability of passing Physics given that they passed Chemistry is 0.6.  The probability of passing Math given that they passed Chemistry is 0.5.  The probability of passing all three subjects is 0.2.

What is the probability that a student passes at least one of the three subjects given that they failed Math?

0.633

Collecting and Interpreting Data

100

The name of a study in which neither the subjects nor the researchers know who is receiving the treatment

Double-Blind Study

200

What variable that has an important effect on the relationship among variables but is not one of the explanatory variables?

Confounding Variable

300

What is the sampling method where researchers divide a population into homogeneous groups and then take a random sample from each group?

Stratified Random Sampling

400

What is the sampling method where the population is divided into heterogeneous groups, and entire groups are randomly selected?

Cluster Sampling

500

What technique is used to ensure that every possible sample of size (n) has an equal chance of being selected to avoid bias?

Simple Random Sampling

Z-Inference Procedures

100

This is the symbol for the parameter of a One Sample Z-test

p (population proportion)

200

The condition(s) required to conduct One Sample Z-tests

Independence AND Approximately Normal

300

What rule makes sure the sample size is appropriate when sampling without replacement.

10% Rule

400

The correct critical values for 90%, 95%, AND 99% confidence intervals.

90% = 1.645

95% = 1.960

99% = 2.576

500

What is the effect on the overall margin of error if you decrease the confidence level from 95% to 90%

The interval becomes smaller

T-Inference Procedures

100

This formula is used to calculate the degrees of freedom (df) for a one-sample t-test given a sample size (n).

n - 1

200

A study measures the weights of 5 individuals before and after a 4-week weight loss program to see if it is effective. The scientists want to measure if there is a significant weight loss by testing participants before and after a diet program.

Identify the type of procedure

A matched-pairs T-test for mean difference

300

The null hypothesis H0 assumes no difference between population means μ1=μ2, while the alternative Ha suggests a difference exists μ1=/ μ2.

H0: μ1=μ2

Ha: μ1=/ μ2

or

H0: μ1-μ2=0

Ha: μ1-μ2=/0

400

Scientists want to compare mean social insight scores between males and females, the data included 133 males x=25.34, s=5.05 and 162 females x=24.94, s=5.10

A 96% confidence interval was (-0.8247, 1.6247)

Make the correct conclusion based on the confidence interval

Since the interval contains zero, the data does not show a significant difference in social insight between genders.

500

A manager wants to know if two locations produce different sized burgers.

Location 1: n=15 patties, x=101 grams, s=3 grams

Location 2: n=12 patties, x=98 grams, s=2 grams

Confidence Level: 95%

Find the interval

3(+-)3.223(.966)

=(1.08,4.92)

Chi squared Inference Procedures

100

The shape of any chi squared test

Skewed right

200

The name of all types of chi squared tests

Goodness of Fit

Homogeneity

Independence

300

This is the type of data used for chi squared tests

Categorical Data

400

A shop owner claims an equal number of customers visit every weekday. He records the count for Monday through Friday. Is the shopkeeper's claim true?

Find the type of inference procedure the shop owner should use

Goodness of Fit Test

500

Name both the degrees of freedom and the expected counts of this problem:

Researchers want to know if having a Netflix subscription is independent of gender.  The data shows the responses of 300 people 

                      Yes       No

    Females      120       30

    Males           90        60

Degrees of freedom: 1  (2-1)(2-1)

Expected counts:

                   Yes      No

Females      105    45

Males        105    45