Module 6

Question 1

What is descriptive statistics?

Answer 1

• any quantifiable characteristic of a sample
• each measurement variable has its own set of descriptive statistics
• labelled using the latin alphabet

Question 2

What are poopulation parameters?

Answer 2

• describe attributes of a statistical population
• quantifiable chaarcteristics

Question 3

Why is the value of a population parameter at the time when a sample is collected considered fixed?

Answer 3

• since the statistical population is the set of all sampling units of interest
• two people collecting the data should get the same thing since it would come from the same population

Question 4

Why is descriptive statistics not fixed?

Answer 4

because two people collecting their own samples would select different sampling units by chance, and end up with different mean values

Question 5

What is estimation?

Answer 5

is the process by which the descriptive statistics of a sample become the population parameters of the statistical population.

Question 6

What is a sampling distribution?

Answer 6

the distribution of some descriptive statistic that would emege if one were to repeatedly draw samples from the statistical population

Question 7

What can sampling distributions be created for?

Answer 7

any descriptive statistic

Question 8

what is a similarity between the sampling distribution and the statistical population?

Answer 8

• they have the same mean value
• one difference is that the sampling distribution is narrower than the statistical population

Question 9

What are two key characteristics of sampling distribution
/

Answer 9

• the shape of a sampling distribution is independent of the statistical population so long as the sample size is sufficiently large
• the variance of a sampling distribution increases as the number of sampling units in the sample decreases

Question 10

What shape does sampling distribution have?

Answer 10

bell shaped

*have to have a large enough sample size

Question 11

What happens as the size of the sample increases in regards to sampling distributions?

Answer 11

as the size of a sample increases, the variance of the sampling distribution decreses.

this is because the larger the sample size, the more accurate the estimate of the mean and the less it varies among repeated samples

Question 12

What is the central limit theorem?

Answer 12

formal development of the principles behind the two key characteristics of sampling distributions

• sampling distributions has a bell shape that is independent from the statistical population
• that the variance of a sampling distribution decreases as the sample size increases

Question 13

What does the central limit theorem add in terms of shape independence?

Answer 13

• the sampling distribution tends toward a normal distribution as the sample size gets larger
• the mean of a sampling distribution is the same as the mean of the statistical population

Question 14

What si the standard error (SE)?

Answer 14

is the standard deviation of the sampling distribution.

Question 15

How can the standard error be calculated?

Answer 15

• calculated from the standard deviation of the statistical population and the sample size

SE=sd/square root of the sample size

Question 16

What is the chain of inference?

Answer 16

a single sample from a statistical population is enough for us to estimate the sampling distribution

Question 17

What is the student’s t-distribution?

Answer 17

• has a shape that depends on the sample size, but also looks similar to a normal distribution
• when sample size is small, the t distribution has fatter tails than a normal distribution to account for te uncertainity in estimating the standard deviation of the statistical population

Question 18

What is the consequence of the inference chain?

Answer 18

the final distribution will be a t distribution rather than a normal distribution

Question 19

What are confidence intervals?

Answer 19

describe the range over the x-axis of a sampling distribution that brackets a certain probability of where new samples may be found

Question 20

What are confidence intervals based on?

Answer 20

t distributions

Question 21

How do we calculate standard t distribution?

Answer 21

• similar to normal distribution calculation
• divide by standard error instead of SD
• x is the raw regular t distribution given
• m is mean

t=(x-m)/SE

Question 22

What are the two steps of calculation of confidence intervals?

Answer 22

• find the intervals on the standardized scale, use the t distribution to find the locations of interest (use tL and tU for upper and lower confidence)
• convert to the standardized t scores from the raw scale.

Question 23

how to calculate raw scale confidence intervals?

Answer 23

xL= m + tL xSE

xU= m + tU xSE

if you want standardized, do the opposite