Multiple Choice + True False

Let X be a continuous random variable with mean 4 and standard deviation 0.2. Then P(X = 4) = 0.0

TRUE. For comtinuous rv there is not mass associate with a single point. That's P(X = a) = 0 for all real values a.

The intersection of two events A and B can be equal to the union of the same two events A and B.

TRUE. If the two events are the same namely A = B.

The p-value can never be smaller than 0, or larger than 1.

TRUE. The p-value is a probability, and probabilities can never be above 1 or below 0.

If a random variable Y only takes on values 0; 0:5; 1; 1:5; 2 it is a discrete random variable.

TRUE. This variable has natural gaps, and so is discrete.

The probability of a single event A must be smaller than or equal to the union of two events A and B.

TRUE: The union will always include the probability of A, B, or both, so it must be larger than just the probability of A alone.

If P(A) = 0.40, P(B) = 0.30 and P(A ∩ B) = 0.12, then A and B are:

independent events

properties about p and r

a) -1 <= r <= 1 b) r is unitless c) if r = 1, X and Y have a perfect positive linear relationship d) if r = -1, X and Y have a perfect positive linear relationship

assumptions of Linear Regression

a) X and Y have linear relationship b) random sample of pairs was taken c) all pairs of data (xi, yi) are independent or (all Ei are independent) d) variance of errors Ei is constant e) average of errors is zero f) errors are normally distributed

assumptions for One Sample CI:

a) random sample

assumptions for Two Sample CI:

a) random sample

assumptions for Goodness of Fit

a) random sample b) ei >= 5 for all groups

assumptions for Wilson Adjusted CI:

a) random sample b) y >= 5 and (n -y) >= 5

assumption for Linear Model:

a) two numeric values X and Y b) X is the explanatory variable that explains the behavior of Y c) Y is the response variable that responds to the change in X

a) nominal b) ordinal c) continuous d) discrete

a) unordered, categories (male, female) b) ordered categories (months, scale 1-10) c) any # in an interval (cm, height) d) natural gap (1,2,3,4,) (money u can hand, # of outbreaks)

coefficient of termination

a) used to access how well our model fits b) r^2 = coefficient of determination

when is CLT used

when not normally distributed

If P(A) = 0.42 and P(B) = 0.38, then P(A ∪ B) is:

Cannot be determined from the given information.

Suppose P(A) = 0.4, P(B) = 0.3, and P(A ∩ B) = 0. Which one of the following statements correctly defines the relationship between events A and B?

Events A and B are mutually exclusive, but not independent.

For a sample dataset, it is not possible for the first quartile to equal the median.

FALSE. If, for example, the entire dataset was the same value repeated, the median and first quartile could equal eachother.

Outliers do not have a strong inuence on the range of a dataset.

FALSE. Since outliers will necessarily be one of the largest or smallest observations, they will have a large influence on the range.

If the sample standard deviation for dataset A is 15, and the sample standard deviation for dataset B is 100, then we may be certain that the mean of dataset A is less than the mean of dataset B

FALSE. The sd measures the spread but does not provide the location of the means/centers.

The standard deviation must always be larger than the mean.

FALSE. The standard deviation gives information about how far away values are from the mean, but no information on the mean itself. You could have a very large mean, but very small standard deviation, for example.

For two events A and B (where Pr{A} > 0, Pr{B} > 0), the following equation holds true: Pr{A|B} = Pr{B|A}.

FALSE. This is not, in general, true. This is because when we switch the event after the conditional, we are changing what subset of the possible events we are looking at.

It is appropriate to use the Empirical Rule for any shape of dataset.

FALSE. It should only be applied to approximately bell shaped data.

The probability of the intersection of two events could be higher than the probability of the union of two events.

FALSE. The union is always at least as larger as the interesection, since the union is "one, or the other, or both

If we have 5 binomial trials, and Y =# of successes in the 5 trials, Y can take on only values 1; 2; 3; 4; 5

FALSE. There could also be zero successes. Therefore, Y could equal 0, 1, 2, 3, 4, 5.

The intersection of two events A and B can be larger than the union of the same two events A and B.

FALSE: The union will always include the intersection, so that the intersection cannot be larger.

If two events are independent, that means PrfA or Bg = PrfA and Bg

FALSE: If two events are indpendent, it means either (i) Pr{A and B} = Pr{A}Pr{B}, or (ii) Pr{A|B} = Pr{A}

The condition probability of A given B must be smaller than the intersection of the same two events A and B

FALSE: It will always be larger, since it is the intersection divided by a number smaller than one.

If the mean value of a set of data is 83.5 and the median is 72.8, then the third quartile will be at least 83.5.

False

Two events A and B are said to be independent if and only if P(A | B) = P(B) or P(B | A) = P(A)

False

assumptions for Anova

-independence assumption -equal variance assumption -Normal population assumption

For a normal random variable Y with mean μY and standard deviation Y , Pr{Y > μY } = Pr{Y < μY }.

TRUE. For a normal random variable, the mean is the median, so 50% lies above it and 50% below.

The minimum possible value that Y can take on where Y is a binomial random variable is the value 0.

TRUE. For any value of n, the smallest number of sucecsses that a binomial random variable can take on is zero (or no successes).

It is possible for the median of a sample dataset and the first quartile of a sample dataset to be the same number.

TRUE. For example the dataset { 2, 2, 2}.

Outliers have a strong inuence on the mean of a dataset.

TRUE. Since the mean equally weights all ovservations in a dataset, outliers tend to change the mean much more than the median.

The 90th percentile is the value for which 10% of the data lies above it.

TRUE. The 90th percentile has 90% below it, so 10% must be above it.

Asking 20 people how old they are. This is an example of non Binomial

True (there can only be two outcomes)

A person can achieve a target 3 out of 4 times. The count of tries is 5. This is an example of Binomial.

True (two outcomes - can achieve or not)

correlaton coefficient

correlation between two variables means they have a linear relationship p (rho) is the population correlation coefficient r is the sample correlation coefficient

CI containing "0" CI not containing "0"

no sig difference in group means sig diff in group means

When Cynthia enters a grocery store, there are three simple events: buy nothing, buy a small amount, or buy a large amount. In this situation, if Cynthia buys a small amount, she cannot also buy a large amount or buy nothing. Thus the three events are:

mutually exclusive