Midterm

Question 1

What is the total area under the density curve?

Answer 1

100% or 1

Question 2

What percent of observations will fall within 1 standard deviation of the mean of an approx. Normal distribution?

Answer 2

68%

Question 3

What percent of observations will fall within 2 standard deviation of the mean of an approx. Normal distribution?

Answer 3

95%

Question 4

What percent of observations will fall within 3 standard deviation of the mean of an approx. Normal distribution?

Answer 4

99.7%

Question 5

What is “r”?

Answer 5

the correlation r measures the strength of a linear relationship

Question 6

What values can r take? What does it mean when r is less than 0?

Answer 6

r can take any value from -1 to 1. If it’s less than zero, it describes a negative correlation.

Question 7

What does it mean when r = 1? r = -1?

Answer 7

perfect correlation/points on a scatterplot lie exactly on a straight line; r = -1 means perfect negative correlation

Question 8

What is the slope b of a regression line y-hat = a + bx?

Answer 8

the predicted change in y-hat when x increases by 1 unit

Question 9

What does the standard deviation of the residuals measure?

Answer 9

typical size of prediction errors when using the regression line

Question 10

What does the coefficient of determination r^2 measure?

Answer 10

fraction of the variation in the response variable that is accounted for by the least-squares regression on the explanatory variable

Question 11

Define influential observations

Answer 11

Individual points that substantially change the correlation or the regression line; outliers are often influential for the regression line

Question 12

The least squares regression line of Y on X is the line with slope B= ? and intercept A = ?

Answer 12

r(Sy / Sx)

YMean - bXMean

Question 13

What are the 4 basic principles of experimental design?

Answer 13

1. Comparison: use a design that compares 2 or more treatments
2. Random assignment: use chance to assign experimental units to treatments. This helps create roughly equivalent groups before treatments are imposed.
3. Control: keep as many other variables as possible the same for all groups. Control helps avoid confounding and reduces the variation in responses, making it easier to decide whether a treatment is effective.
4. Replication: impose each treatment on enough experimental units so that the effects of the treatments can be distinguished from chance differences between the groups.

Question 14

Describe a randomized block design

Answer 14

A randomized block design forms groups of experimental units that are similar with respect to a variable that is expected to affect the response. Treatments are assigned at random with in each block. Responses are then compared with in each block and combined with the responses of other blocks after accounting for the differences between the blocks.

Question 15

Describe a matched pairs design

Answer 15

A matched pairs design is a common form of blocking for comparing just two treatments. And some matched pairs designs each subject receives both treatments in a random order. And others to very similar subjects are paired and the two treatments are randomly assigned within each pair

Question 16

What makes something a simple random sample?

Answer 16

It gives every possible sample of the same size an equal chance to be selected

Question 17

How should you organize a matched pairs experiment?

Answer 17

Subjectively divide the sample into pairs to make the pairs as similar to each other as possible, and then randomly assigned the treatment to one of the members of the pair

Question 18

What is the law of large numbers?

Answer 18

The law of large numbers says that the proportion of times that a particular outcome occurs in many repetitions will approach a single number.

Question 19

What will the probability of the sample space always equal?

Answer 19

1

Question 20

What is the addition rule for mutually exclusive events?

Answer 20

P(A or B) = P(A) + P(B)

Question 21

What probability does the union of A and B describe?

Answer 21

P(A or B)

Question 22

What probability does the intersection of A and B provide?

Answer 22

P(A and B)

Question 23

What is the general addition rule to find P(A or B)?

Answer 23

P(A or B) = P(A) + P(B) - P (A and B)

Question 24

What does the general multiplication rule state?

Answer 24

P(A and B) = P(A) * P(B | A)

Question 25

If two events are mutually exclusive, they can/cannot be independent

Answer 25

Cannot

Question 26

What are the sums of the means of X + Y?

Answer 26

X mean + Y mean

Question 27

What are the variance of X + Y?

Answer 27

variance X + variance Y

Question 28

What are the variance of X - Y?

Answer 28

variance X + variance Y

Question 29

What are the qualifications of a binomial setting?

Answer 29

Binary- The possible outcomes of each trial can be classified as a success or failure
Independent- trials must be independent; that is, knowing the result of one trial must not tell us anything about the result of any other trial
Number- The number of trials of the chance process must be fixed in advance
Success- there is the same probability of success on each trial

Question 30

What is the 10% condition?

Answer 30

The binomial distribution gives a good approximation to the count of successes in a simple random sample from a large population containing proportion P of success. This is true as long as the sample size is no more than 10% of the population size.

Question 31

What is the large counts condition?

Answer 31

You can use a normal approximation for a binomial distribution when the sample size times the probability of success is greater than 10 and the sample size times the complement of the probability of success is also greater than 10

Question 32

How do you find the geometric probability?

Answer 32

P(Y=k) = (1-p)^(k-1) (p)

Question 33

How do you find a mean or expected value of a geometric random variable?

Answer 33

The mean is equal to one divided by the probability of success

Question 34

The central limit theorem states that when n is ?, the sampling distribution of XBar will be approx. Normal in most cases

Answer 34

n > or = 30