lecture 3. statistical inference

Question 1

does this describe exploratory data analysis or statistical inference?
its purpose is unrestricted exploration of data, searching for interesting patterns; conclusions apply to the subjects and circumstances for which we have data in hand; conclusions are informal based on what we see in the data

Answer 1

exploratory data analysis

Question 2

does this describe exploratory data analysis or statistical inference?
purpose is to answer a specific question, posed before the data produced; conclusions apply to a larger group of subjects or a broader class of circumstances; conclusions are formal, backed by a statement of our confidence in them

Answer 2

statistical inference

Question 3

this is a method for drawing conclusions about a population from a sample. uses probability to indicate how trustworthy its conclusions are. assumes a random sample - if this is not the case your conclusions may be faulty

Answer 3

statistical inference

Question 4

what are the two most common types of statistical inference?

Answer 4

• significance tests
• confidence intervals

Question 5

this common type of statistical inference estimates a population parameter.

Answer 5

confidence intervals

Question 6

this common type of statistical inference assess the evidence in the data for some claim about the population

Answer 6

significance tests

Question 7

generating statistics from a relatively small sample to provide an indication of a population value (parameter) is the process of ________

Answer 7

estimation

Question 8

________ are fixed for a given population (the mean for a given population is constant)

Answer 8

parameters

Question 9

_______ are estimates of parameters and cary sample by sample. in effect they are random variables.

Answer 9

sample statistics

Question 10

the ____________ distribution is the distribution of all possible values of that statistic in all possible random sample so the same size n from population N

Answer 10

random sampling

Question 11

if a random variable x has a population mean μ and population variance σ2, then the sampling distribution of means (of samples of size n) will have a mean of μ and variance ____

Answer 11

σ2/n

Question 12

this property means variability of the random sampling distribution depends on _______ and ________

Answer 12

sample size and the variability of the population

Question 13

the ______ (smaller/larger) the sample size, the smaller the σ2/n

Answer 13

larger

Question 14

_______ (more/less) variance = the more certain we can be

Answer 14

less

Question 15

since sample means are normally distributed, we can define a ________ which is a range of values used to estimate the true value of the population parameter; it is the probability (usually expressed as a percentage) or the proportion of times that the ____ actually does contain the population parameter

Answer 15

confidence interval (CI)

Question 16

states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed.

Answer 16

central limit theorem

Question 17

In a sample mean, we use the _______ to describe the variability of individual observations

Answer 17

standard deviation, σ

Question 18

in a sample mean, we use the ______ to describe the variability of a sampling distribution

Answer 18

standard deviation of the sampling distribution of means/THE STANDARD ERROR OF THE MEAN

Question 19

For normal distributions, μ +/- σ contains 68.26% of the observations, μ +/- 2σ contains 95.44% of the observations and so on based on the empirical rule. How does this statement differ for a Sampling distribution?

Answer 19

For normal distributions, μ +/- σ contains 68.26% of the observations, μ +/- 2σ contains 95.44% of the observations, etc.

For sampling distribution, mean +/- σ/√n contains 68.26% of the observations, mean +/- 2σ/√n contains 95.44% of the observations, etc.

Question 20

what are the SIX steps in hypothesis testing

Answer 20

1. state the null hypothesis
2. state the alternative hypothesis
3. set the decision level (alpha)
4. choose the test statistic
5. calculate P (assumes null hypothesis is true)
6. make a decision concerning null hypothesis

Question 21

this states that any differences in the data are due to chance

Answer 21

null hypothesis

Question 22

this states that any differences in the data are “real’ or significant

Answer 22

alternative hypothesis

Question 23

if P (null hypothesis is true) is less than 0.05, do you reject or retain the null hypothesis

Answer 23

reject null hypothesis

Question 24

if P (null hypothesis is true) is greater than 0.05, do you reject or retain the null hypothesis

Answer 24

retain the null hypothesis