Quantitative Skills Workshop

Question 1

Manipulating Exponents: x^-a –> ?

Answer 1

1/x^a

Question 2

Manipulating exponents: x^a*x^b —> ?

Answer 2

x^(a+b)

Question 3

Manipulating exponents:

x^1/a –> ?

Answer 3

asqrt

Question 4

Manipulating logarithms:

log(1) = ?

Answer 4

0

Question 5

Manipulating logarithms:

log(x*y) = ?

Answer 5

log x + log y

Question 6

Manipulating logarithms:

log(x/y) = ?

Answer 6

log x - log y

Question 7

Manipulating logarithms:

log(x^y) = ?

Answer 7

y log x

Question 8

Calculus concepts:

To find the derivative on a graph, what should you look at?

Answer 8

The slope of the line or the slope of a curve at a certain region

Question 9

Calculus concepts: To find the integral of a graph, what should you look at?

Answer 9

The area under the curve

Question 10

To find inflection points given an equation, what should you do?

Answer 10

Take the second derivative and set it equal to zero.

Question 11

How can you determine whether the location of your inflection point is a local maximum (apex) or minimum?

Answer 11

Check for concavity at the left and right of your inflection point. For a maximum you should go from a positive to negative slope and for a minimum you should go from a negative to a positive slope. at the inflection point.

Question 12

What are the 4 data types?

Answer 12

Sample vs population data and quantitative vs qualitative data

Question 13

What are some statistical tools to measure centers of data?

Answer 13

Mean, median and mode

Question 14

How can you measure variance?

Answer 14

By looking at the range or variance

Question 15

List 4 types of normal distributions.

Answer 15

Mean, standard deviation, standard error and confidence intervals.

Question 16

What are 3 types of hypothesis testing?

Answer 16

Null-hypothesis, p-value, statistical significance

Question 17

What is single variable regression?

Answer 17

?

Question 18

What are the two types of qualitative or categorical data?

Answer 18

Nominal and ordinal

Question 19

Define nominal data.

Answer 19

Has a label with no numerical value or order

Question 20

Define ordinal data.

Answer 20

Labels can be ordered or ranked, but do not have exact numerical meaning

Question 21

What are two types of quantitative data?

Answer 21

Interval and ratio

Question 22

Define interval data.

Answer 22

Contains numerical values such that the interval (space between numbers) is precisely defined

Question 23

Define ratio data.

Answer 23

Contains numerical values such that the interval is precisely defined and the number zero has meaning

Question 24

Define mean, median, and mode.

Answer 24

Mean: the average of all measured values
Median: the middle measurement of a data set when arranged in numerical order
Mode: the most frequently occurring value

Question 25

What is the purpose of a confidence interval?

Answer 25

To make a statement that we are confident that the population mean is somewhere within an interval around the sample mean

Question 26

The standard deviation plus what range of values covers the margin of error?

Answer 26

The standard deviation +/- the critical value [(Z)^(-a/2)] times the standard error [s/sqrt(n)] is the margin of error, as shown in the image on slide 16 of the Quantitative Skills Workshops.

Question 27

Describe null hypothesis.

Answer 27

The null hypothesis is denoted by Ho and is assumed to be true unless proven otherwise.

Question 28

Given a sample size n, a mean of x and a sample standard deviation of s, what is the overall standard deviation?

Answer 28

s/sqrt(n), where s is the sample standard deviation and n is the sample size.

Question 29

What does the p value describe?

Answer 29

The probability that the sample comes from a population where the null hypothesis is true.

Question 30

Describe the linear correlation coefficient.

Answer 30

The linear correlation coefficient is denoted by r and is tells us how close the relationship (graph trend) is to a line. The closer to 1, the more linear it is.

Question 31

What is the coefficient of determination?

Answer 31

The coefficient of determination is r^2, and it tells us variability in the data from the best fit line. The closer r^2 is to 1, the better the fit.