Test II

What are the 3 conditions for binomial distribution

1. Each trial has 2 outcomes

2. Each trial has same probability of success

3. Trials are independent to each other

Binomial equation

When ur asked to find the probability distribution, what r u finding?

1) List all possible outcomes AND 2) the probability of each outcome

ex: a bar graph (spaces b/w) or table

What is X?

Ex: X = the number of times a 4 is rolled, rolling three times

Ex: X = 0, 1, 2, 3,

Every distribution follows which two rules?

1. P is between 0 and 1

2. the sum of the probabilities is 1

just A, B, C

6.4 A

6.5

2. 25/500

3. 25/916

Given that there is a 50% baseline chance of innocence before looking at the DNA evidence, a DNA match makes the probability that Jane Doe is actually innocent extremely small (approximately \(0.00000101\)). This means it is almost certain she is guilty under these conditions.

What are the 6 formulas

draw the general tree diagram

what is sensitivity

true positive

what is specificity

true negative

Three rules for independence

Total outcomes #

multiple individual outcomes for each

ex: roll a die, flip a coin, roll a die = 6×2×6

write all the 6 formulas

Three rules for checking for independence

1. P(A|B) = P(A)

2. P(B|A) = P(B)

3. P(A and B) = P(A) * P(B)

how to get the total number of outcomes

multiply all the individual outcomes together for each

ex: roll a die, flip coin, roll a die

(2)(2)(2)

another ex: 10 question T or F test

2^10 (bc there are 2 answers and 10 questions)

Intersection

AND, both things must be true at the same time

Union

OR

Disjoint

probability of rolling a one AND no one’s (0/36) given 2 dice

Positive association

big exp variable = big response variable

Negative association

big exp variable; small response variable

Correlation formula

correlation only if there’s a __ line between the 2 variables

correlation only if there’s a straight line between the 2 variables

What does the correlation coefficient do?

What does the regression line do?

• Correlation coefficient: how strong an association is

• Regression line: predicts y-values when missing data

Residual definition and formula

• point on line where observation would lie

• actual - expected

extrapolation

prediction a variable value outside of the data set and expecting the trend to continue

for regression line, can you swap the x and y variables? Can you for the correlation coefficient?

Yes for correlation and no for regression

2 things that must be true to have influential outlier

1. If x-value is high or low compared to the rest of the data

2. if observation doesn’t lie close to the regression line

The following graph shows data on x = the number of televisions per 100 people and y = the birth rate (number of births/1,000 people) for 6 African and Asian countries. The regression line, y = 29.8 - 0.024, applies to the data for these 6 countries. Another point is added at (81,15.2), which is the observation for the United States. The regression line is y = 31.2 = 0.195x for all seven points.

A. Does the US observation appear to be an outlier on (i) X, (ii) Y, (iii) outlier relative to the regression line of the 6

B. State the two conditions under which a single point can have a dramatic effect on the slope and show that they apply here

C. This one point also drastically affects r (-0.051 without the US and -0.935 with the US). Explain how the relationship between birth rate and the number of televisions is (i) without the US point and (ii) very strong with the US point

D. Explain why the US residual for the line fitted using that point is very small.

The following table shows data on gender (1 = female, 2 = male) and preferred chocolate type (1 = white; 2 = milk; 3 = dark) for a sample of 10 students.

The teacher enters the data into a software and reports a correlation coefficient of 0.640 between gender and chocolate preference, he concludes there’s a strong, positive linear relationship between the two. What’s wrong with this analysis?

Mountain bike information (move on to next problem)

3.43 [TRY] [APP] Mountain bike and suspension type Refer to the previous exercise. In addition to weight and price, the data file also contains information on the type of suspension of the bike .

1. The following scatterplot, obtained via the Multivariate Relationships app, colors the dots by suspension type. Is the single regression line fitted in the previous exercise the best way to describe the relationship between weight and price?

2. Using the app or other software, find separate regression equations for the two suspension types. Summarize your findings.

3. The correlation coefficient for all 12 data points is If the correlation coefficients for the full and front-end suspension bikes are found separately, how do you believe they will compare to ? Find them and interpret. (Hint: The Multivariate Relationships app allows you to find r and for each suspension type separately.)

4. You see a mountain bike advertised for $700 that weighs 28.5 lb. The type of suspension is not given. Would you predict that this bike has a full or a front-end suspension? Statistically justify your answer.