Estimating with Uncertainty

Question 1

estimation

Answer 1

process of inferring a population parameter from sample data

Question 2

how does the estimation of a parameter reflect the population parameter

Answer 2

almost NEVER the exact same as the value of the population parameter being estimated

Question 3

what do we want to know about the estimate of a sample

Answer 3

how precise it is (how close to the true value in the population it is)

Question 4

sampling distribution

Answer 4

probability distribution of all the values for an estimate that we MIGHT have obtained when sampled the population

Question 5

what is the sampling distribution used to determine

Answer 5

how precise the estimate is

Question 6

what does sampling distribution represent

Answer 6

the “population” of values for an estimate

Question 7

how does the spread of sampling distribution depend on sample size

Answer 7

Larger the sample size = the narrower the sampling distribution = the more precise the estimate

Question 8

standard error reflects

Answer 8

differences between an estimate and the target parameter = reflects the precision of an estimate

Question 9

smaller vs larger standard error

Answer 9

smaller = more precise estimate

larger error = less precise estimate

Question 10

what is the relationship between standard error and sample size

Answer 10

as sample size INCREASES the standard error DECREASES

Question 11

Confidence intervals is used because it

Answer 11

Quantifies uncertainty about the value of a parameter

Question 12

what are confidence intervals

Answer 12

Range of numbers surrounding the sample estimate that is likely to contain the unknown value of the population parameter

Question 13

what is the 95% confidence interval for the mean

Answer 13

A range likely to contain the value of the true population mean which extends above and below the sample mean

Question 14

what do the numbers between the upper and lower bounds for a confidence interval represent

Answer 14

most plausible values for the parameter

Question 15

Values OUTSIDE the confidence interval are

Answer 15

less plausible for the true value of the parameter in the population

Question 16

Width of the 95% confidence interval

Answer 16

measure of uncertainty about the true value of the parameter

Question 17

broad vs narrow confidence interval width

Answer 17

broad = uncertainty is high = data not informative about location of population parameter

narrow = uncertainty is low = data is informative about the location of population parameter

Question 18

how is the approximate of the 95% confidence interval for mean population calculated

Answer 18

adding (upper limit) or subtracting (lower limit) two standard errors from the sample mean

Question 19

Error bars

Answer 19

Lines on a graph extending outward from the sample estimate that illustrates precision of an estimate

Question 20

Y bar is the estimate of

Answer 20

mu (population mean)

Question 21

s is the estimate of

Answer 21

sigma (population standard deviation

Question 22

P hat is the estimate of

Answer 22

p the population proportion

Question 23

what must be known for estimates to be useful

Answer 23

the precision of said estimates

Question 24

what is the process of estimation

Answer 24

the process of inferring a population parameter from sample data

Question 25

are estimates often the same as the population parameters

Answer 25

NO - chance events make samples different from the true pop parameter

Question 26

sampling distribution of the estimate

Answer 26

probability distribution of ALL values for an estimate we MIGHT have obtained when sampling the population REPEATEDLY

Question 27

sampling distribution of sample mean

Answer 27

sampling distribution = the probability distribution of values (for mean) that we MIGHT of obtained when sampling population repeatedly

Question 28

what is key in regards to the sample mean distribution

Answer 28

the true value of the population (mu) is a CONSTANT - has one distinct value while the sample mean is a VARIABLE - changes with every sample distribution taken

Question 29

when is the y bar sample unbiased

Answer 29

when it corresponds to mu (represents the exact value of the pop parameter)

Question 30

how does sample size affect sampling distribution of mean

Answer 30

larger sample = narrower sample distribution = more precise the population estimate

Question 31

standard error

Answer 31

for an estimate its the standard deviation of the estimate’s sampling distribution

Question 32

are large or small standard errors more precise

Answer 32

small errors = smaller standard deviation of data = values are tightly clustered around the true value

Question 33

how to calculate Standard error of the sample mean (SEM)

Answer 33

SAMPLE standard deviation of variable Y divided by the sample size

Question 34

confidence interval

Answer 34

range of values that surround a sample estimate that is LIKELY to contain the population parameter (but NOT ALWAYS)

Question 35

95% confidence interval of the mean

Answer 35

range, extending above and beyond the sample mean, likely to contain the mean population parameter (mu)

Question 36

can all numbers in the 95% C.L be plausible for the true value

Answer 36

YES - 95% CI does not give the EXACT value but a range that it COULD be in

Question 37

are narrower or wider CI’s more informative

Answer 37

narrower = more information for pop true value

Question 38

error bars

Answer 38

lines that extend from sample estimates that give information about the precision of the estimate