ch 12 - Data-based and statistical Reasoning

Question 1

measures of central tendency

Answer 1

those that describe the middle of a sample; how middle is defined can be different

Question 2

mode

Answer 2

number that appears most often in a set of data

Question 3

normal distribution

Answer 3

mean, median and mode are at center of distribution

Question 4

standard distribution

Answer 4

mean is zero and standard deviation of one

Question 5

skewed distribution

Answer 5

contains a tail on one side or the other of the data set. Negatively skewed is tail to the left with mean lower than median and positively is tail to the right with mean higher than median

Question 6

bimodal

Answer 6

distribution containing two peaks; do not have to have two modes.

Question 7

range

Answer 7

difference between data set’s largest and smallest values

Question 8

interquartile range

Answer 8

related to the median, first and third quartiles; gathered by subtracting the value of the first quartile from the value of the third quartile (IQR = Q sub 3 - Q sub 1)

Question 9

quartiles

Answer 9

include median (Q sub 2), divide data when placed in ascending order into groups that comprise one-fourth of the entire set; first quartile is 1/4n (number of data) and mean of number at whatever position that is and the number of the next position.

Question 10

example of using interquartile range to determine outliers

Answer 10

find range which is third quartile - first quartile. Use this range to multiply times 1.5 and add this number to third quartile. Anything above this number is an outlier. Use range to multiply times 1.5 and subtract this number from first quartile - anything falling below this number is an outlier

Question 11

standard deviation

Answer 11

calculated by taking the difference bt each data point and the mean, squaring this value, dividing the sum of all of these squared values by (the number of points in the data set minus one (so divided by n-1)), and taking the square root of the result

Question 12

determining outlier via standard deviation

Answer 12

after standard deviation is determined, if a value falls more than 3 x standard deviations outside of mean, it is an outlier.

Question 13

standard deviation and normal distribution

Answer 13

68% of data points fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99% fall within three standard deviations

Question 14

independent events in probability

Answer 14

events that have no effect on one another

Question 15

dependent events in probability

Answer 15

have an impact on one another, such that the order changes the probability

Question 16

mutually exclusive outcomes

Answer 16

cannot occur at the same time; probability of them occurring together is 0%

Question 17

exhaustive outcomes

Answer 17

a group of outcomes that is all inclusive so that there are no other possible outcomes

Question 18

calculating independent probability

Answer 18

P(A) x P(B) - probability of the first option x probability of the second option equals probability that both will occur

Question 19

probability of at least one of two events occurring

Answer 19

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

Question 20

hypothesis testing

Answer 20

begins with an idea about what may be different bt two populations

Question 21

null hypothesis

Answer 21

always a hypothesis of equivalence; says that two populations are equal, or that a single pop can be described by the parameter equal to a given value; when able to rejected based on p-value being greater than significance level (alpha), it means results are statistically significant

Question 22

alternative hypothesis

Answer 22

may be nondirectional meaning that the populations are not equal, or directional

Question 23

z- or t-tests

Answer 23

most common hypotheses; rely on standard distribution or the closely related t-distribution

Question 24

test statistic

Answer 24

calculated and compared to a table to determine the likelihood that that statistic was obtained by random chance (under the assumption that our null hypothesis is true)

Question 25

type 1 error

Answer 25

represented by value of alpha which is the level of risk we are willing to accept for incorrectly rejecting the null hypothesis, meaning we report a difference between two populations when one does not actually exist

Question 26

type II error

Answer 26

we incorrectly fail to reject the null hypothesis; we determine there is no difference between two populations when one actually does exist; probability of this type of error is sometimes symbolized by beta

Question 27

power

Answer 27

probability of correctly rejecting the null hypothesis and reporting a difference between pops when one does exist; equal to 1-beta (1 - type II error)

Question 28

confidence

Answer 28

probability of correctly not rejecting the null hypothesis and reporting that two pops are equal when they actually are.

Question 29

confidence intervals

Answer 29

the reverse of hypothesis testing; determine a range of values from the sample mean and standard deviation; rather than finding p-value, we begin with a desired confidence level and use a table to find its corresponding z- or t-score. We then create a range based on this score x standard deviation by subtracting and adding it to the mean

Question 30

p-value

Answer 30

test statistic compared to a table

Question 31

slope

Answer 31

m = rise/run = delta y/delta x = (y sub 2 - y sub 1)/x sub 2 - x sub 1)