Module 3

Question 1

statistical inference

Answer 1

idea of using sample data to provide evidence about population parameters

Question 2

what can we use to estimate unknown population parameters?

Answer 2

1. Point estimates
2. confident intervals

Question 3

point estimate

Answer 3

single value used as an estimate of a population parameters

Question 4

Xbar

Answer 4

sample mean

Question 5

u

Answer 5

population mean

Question 6

________ the sample mean is a point estimate of _________

Answer 6

xbar sample mean is a point estimate of u the population mean

Question 7

s^2

Answer 7

sample variance

Question 8

o^2

Answer 8

population variance

Question 9

_______ the sample variance is an estimate of ______________

Answer 9

s^2 the sample variance is a point estimate of the o^2 the population variance

Question 10

s

Answer 10

sample standard deviation

Question 11

____ the sample sd is a point estimate of ______________________

Answer 11

s the sample sd is a point estimate of o the population sd

Question 12

what are point estimates influenced by ?

Answer 12

sampling error

Question 13

the variation of a point estimate from one sample to another represents the extent of ___________________

Answer 13

sampling error

Question 14

Sampling error in relation to sample size

Answer 14

Smaller samples have more sampling error than larger samples so we expect point estimates from small samples to have more sampling error than point estimates from larger samples

Question 15

formula for the standard error of the mean

Answer 15

represents the amount that the sample means are spread around the population mean of a variable - or amount that a sample mean is expected to differ from the population mean on average

oxbar = o/sqrtN

the bigger N gets the smaller oXbar gets - mean has less sampling error with larger N

Question 16

confidence interval

Answer 16

range of values or an interval that is expected to capture a population parameter of interest with some prespecified level of confidence

presents a range of plausible or reasonable values for the population parameter

Question 16

Confidence limits

Answer 16

specify the particular range of values for a confidence interval

smallest value = lower limit
biggest value = upper limit

Question 17

confidence intervals in relation to sample size

Answer 17

confidence intervals from small samples are wider than confidence intervals from larger samples

Question 18

central limit theorem tells us that the sample means can be treated as observations from a _____________

Answer 18

normal distribution

Question 19

95% of all sample means fall within _______ standard error units of the population mean

Answer 19

1.96 standard error units of the population mean

Question 20

the 95% confidence interval is expressed as what formula

Answer 20

Xbar +/- 1.96*oxbar

where 1-alpha is the level of confidence

oxbar is also (o/sqrtN)

Question 21

Zalpha is what

Answer 21

critical valye

Question 22

Critical value for a 95% confidence interval

Answer 22

1.96

Question 23

Assumptions for a confidence interval calculated using the standard normal distribution

Answer 23

1. Independent observations
2. The sample data come from a normal population
3. The population standard deviation is known

Question 24

Assumptions for CI 1. Independent observations

Answer 24

- Having info about one participant provides no further info about another participant

Question 25

Assumptions for a CI 2. The sample data come form a normal population distribution

Answer 25

Because of the central limit theorem, this assumption can be ignored as long as the sample size is large. How large depends on the extend of non-normality of the population distribution of individuals.

Question 26

the width of a confidence interval represents _________

Answer 26

the precision of a point estimate with respect to its estimation of the corresponding parameter

Question 27

Does the population mean change?

Answer 27

The population mean is a constant, fixed, but unknown value that does not change.

Question 28

Does the confidence interval change?

Answer 28

The lower and upper confidence limits are random variables meaning they do change from sample to sample

Question 29

If you have calculated a 95% confidence interval how do you phrase it

Answer 29

if the exact sampling procedure were repeated an infinite number of times and a 95% confidence interval were calculated around each sample, 95% of those intervals would contain u. The interval of blank to blank is one of these infinitely many intervals. Easier: The interval captures u with 95% confidence The interval blank to blank captures the population mean number of drinks per week with 95% confidence

Question 30

Factors affecting the width of a confidence interval that are under the researcher's direct control

Answer 30

1. Level of confidence - larger values of 1- alpha have wider intervals 2. Sample Size - larger samples lead to narrower confidence intervals

Question 31

Null hypothesis

Answer 31

represents another method for researchers to describe sample evidence about the true value of a population mean "We reject the null hypothesis that the population mean equals 0 with probability = alpha that we are incorrect

Question 32

want to know whether a mean is different enough to conclude what

Answer 32

conclude that the population mean of home schooled 4th graders is likely to be different from 250 if the population mean is u=250 how unlikely is a sample mean of xbar=272 or more extreme

Question 33

Formal steps of a null hypothesis testing procedure

Answer 33

1. Specify the null hypothesis 2. Specify an alpha level - 0.05 3. Calculate a test statistic - convert sample mean to z score xbar-uo/o/sqrtN 4. Calculate a P-value - probability of obtaining a score greater or equal to the one we are comparing to 5. Compare the p-value alpha/2 to reach a decision about the null hypothesis - two tailed test = have to divide alpha by 2

Question 34

alternate hypothesis example

Answer 34

the population mean achievement score of home-schooled 4th graders does not equal 250 Non-directional which implies a two-tailed test

Question 35

alpha level

Answer 35

probability of rejecting a true null hypothesis

Question 36

test statistic

Answer 36

value calculated from a sample descriptive statistic that is used to evaluate the descriptive statistic relative to the population value specified by the null hypothesis

Question 37

Does the p-value demonstrate the probability that the null is true?

Answer 37

NO

Question 38

Correct interpretation of the p-value

Answer 38

Probability of obtaining the current sample mean or one that is more extreme under the assumption that the null is true.

Question 39

Assumptions of one sample z-test

Answer 39

1. independent observations 2. sample data come from a normal population distribution 3. the population SD is known

Question 40

Effect size

Answer 40

difference between the sample mean compared to the hypothetical population mean idea of by HOW MUCH a null hypothesis is likely to be wrong

Question 41

Does statistical significance convey practical importance?

Answer 41

no, effect size does