Lecture 4.2 Sample estimation

Question 1

why do we draw a sample from a population?

Answer 1

cheaper and easier than measuring the entire population

Question 2

what does a sampling strategy depend on?

Answer 2

the sample being representative of the population

Question 3

what is a population?

Answer 3

group of individuals where we wish to measure a variable of interest

Question 4

what is a population parameter?

Answer 4

summary values from populations e.g means ect

Question 5

what is a sample?

Answer 5

subset of a population

Question 6

whats an underlying assumption from a sample?

Answer 6

sample is drawn at random

values in the sample are independent

Question 7

what does accuracy mean?

Answer 7

Free from bias

• sample means should be measured from the same samples within the same population
• results would ideally be centered around the true population mean

Question 8

what does precision mean?

Answer 8

Repeat-ability

-sample means calculated from repeated samples of the same population and should show little variation

Question 9

When is accuracy affected?

Answer 9

when we are affected in our ability to select a truly representative sample

Question 10

when is precision affected?

Answer 10

depends on sample size and population variance

Question 11

when is a statistic used to estimate a parameter unbiased?

Answer 11

mean of the sampling distribution is equal to the true value of the parameter being measured

Question 12

what is the variability of a statistic ?

Answer 12

spread of its sampling distribution

Question 13

what is a high bias?

Answer 13

spread away from the true value

Question 14

what is high variability?

Answer 14

the data not being close together

Question 15

how can you reduce variability and bias?

Answer 15

random sample

large sample size

Question 16

what is the sample distribution?

Answer 16

frequency distribution of a statistic over an infinite samples of a given size from a population

Question 17

what does the sample distribution represent?

Answer 17

how far the sample mean is from the population mean for any randomly selected sample

Question 18

what does the sample distribution show as the sample size increases?

Answer 18

sample distribution of the mean should show a normal distribution

Question 19

what is the standard error?

Answer 19

standard deviation of the sampling distribution

Question 20

what does the standard error measure?

Answer 20

measures precision in terms of how much any sample statistic varies from one sample to another

Question 21

why cant we usually determine the sampling distribution of the mean?

Answer 21

population is not known

Question 22

what do we do as we cannot determine the sampling distribution?

Answer 22

Sample mean would estimate the unknown population mean

Sample standard deviation would estimate the standard error.

Question 23

how is standard error calculated?

Answer 23

sample standard deviation dividied by the square root of the sample size

Question 24

when will the mean of the sample distribution take the form of normal distribution?

Answer 24

large sample size n>30

irrespective of the distribution of the variable in the population

Question 25

what does central limit theorem allow?

Answer 25

allows the sampling distribution of a statistic to be approximated from a sample

Question 26

what two things affect the range of the confidence interval?

Answer 26

variation –> less variation means a smaller confidence interval
sample size –> larger sample size means a smaller confidence interval

Question 27

what does a 95% confidence interval mean?

Answer 27

95% of repeated samples from this population will produce a plausible range of values which include the population parameter

Question 28

what happens when the sample size is less than 30

Answer 28

central limit theorem is no longer valid

Question 29

what is the student t-test and when do you use it?

Answer 29

when <30 samples
t-test applied with n-1 degrees of freedom (number of observations -1)
VARIABLE OF INTEREST MUST BE NORMALLY DISTRIBUTED IN THE POPULATION