UNIT 6 means inference

Question 1

What are the conditions that have to be met in order to use a normal model for the distribution of sample proportions? (sampling distribution of proportions).. (the distribution of p-hats)..

Answer 1

1. Random and independent
2. Not too large, less than 10% of population, so 10n>N
3. Success/Failure: np>10 and nq>10 (must show calculation)

This lets us use the normal model. Too large samples have sampling distributions that are leptokurtic (narrower and taller than normal model), too small samples have skewed or other shaped sampling disributions.

Question 2

What are the conditions that have to be met in order to use a t-model for the distribution of sample means? (sampling distribution of means).. (the distribution of x-bars)..

Answer 2

1. Random and independence
2. Not too large, less than 10% of population, so 10n>N
3. Not too small, n>30.

OR WITH SMALL SAMPLE as long as it came from a normalish population

Question 3

What is a 2 sample t interval?

Answer 3

Suppose you were trying to find the difference between the IQ of math teachers and IQ of English teachers. You sample 50 of each and find math xbar= 125 and English xbar=115. So, the difference of the samples is 10 points. That is your statistic. 10 points. You now have to add on a margin of error, let’s say.. 4. so, youll say something like “I’m 90 % confident that math teachers score between 6 and 14 points higher on IQ tests.”

Question 4

How do you POOL with PROPORTIONS?

Answer 4

You combine the two samples into one big sample.

TOTAL # RED BEADS / OVERALL TOTAL OF ALL BEADS

Question 5

What are null and alternative for paired tests?

Answer 5

Ho: Md = 0,

Ha: Md > 0.

One sample procedures on list 3.

Question 6

Do alpha and beta work with means?

Answer 6

Yep, alpha, beta, power, type 1, type 2 all go along with means and proportions

Question 7

Do you pool with means (t test)?

Answer 7

you don’t have to do it. Only have to pool with hyp tests for props. Pooling with means is a nasty process, if you think the populations have similar variances, then have your calculator pool for you.

Question 8

how are 2 samp t and paired t different?

Answer 8

2 samp t you are loooking at a difference between 2 averages from 2 distinct sample. With a paired test you make a SINGLE LIST OF DIFFERENCES from each pair, you then look at the AVERAGE DIFFERENCE, the average of a bunch of differences (generally 2 measurements on just ONE sample).

Question 9

Simple quick way to describe difference between paired T and 2 sample T.

Answer 9

Paired T looks at average of differences,

2 sample T looks at the difference of averages.

Question 10

Where did Bill Gossett work?

Answer 10

GUINNESS

Question 11

What did Bill Gossett Do?

Answer 11

He sat on the Normal model and made some tea.

(Tmodel looks like someone sat on the normal model)

Question 12

how are t models like Normal models?

Answer 12

both are unimodal and symmetric. T models aren’t as high and have more area in tails, that’s why you have to reach out a little further than z for same confidence, or be a little further away for significance. Bill sat on the normal model.

Question 13

how can you decide the right test?

What are the 3 questions?

Answer 13

1 or 2 samples?

Proportions (z) or Means (t)? (categories or numbers?)

Test or Interval?

Question 14

how do you check nearly normal for small samples?

Answer 14

Histogram on calculator of the sample,

or normal prob plot on calculator (is it diagonal?), .

or Boxplot (is it symmetric?)

Question 15

how do you find deg freedom?

Answer 15

n-1 for one sample

2 samples you must use calculator..

REGRESSION IS n-2

Question 16

How do you find degrees of freedom for 2 sample mean stuff?

Answer 16

MUST USE CALCULATOR

Question 17

How do you calculate SAMPLE SIZE with proportions?

Answer 17

n = Z²pq / ME²

Question 18

How do you calcuate SAMPLE SIZE with means?

Answer 18

n= (t*s/n)²

ForfFirst calculation, use Z crit.. Then go through and calculate n.. Use that n for a t crit and do it again. Takes a couple cycles to settle down.

Question 19

What is the quick sample size calculation for proportions?

Answer 19

1 / ME²

Question 20

How do you find df in 2 samples? What is odd procedure by hand?

Answer 20

you have to run an interval or a test on your TI first, and read the output to get df, then do it by hand… ugh.

Question 21

how do you find z and t crit?

Answer 21

for z crit:. INVNORM(area in 1 tail)

for t crit:. INVT(area in 1 tail, deg freedom)

Question 22

If you were going to pool with means (t), which you probably won’t have to do, when would you?

Answer 22

When you have reason to believe the variances of both populations are equal.

Question 23

what are the conditions that have to be met for t procedures with small samples?

Answer 23

independent groups, random, <10% of pop and nearly normal.

Question 24

what happens to t models as n gets larger?

Answer 24

The models look more like the normal model. An infinite sample size would give a t model identical to the normal model.

Question 25

What is a 2 sample t interval?

Answer 25

You are trying to catch the true difference between two group’s averages.Suppose you were trying to find the difference between the IQ of math teachers and IQ of English teachers. You sample 50 of each and find math xbar= 125 and English xbar=115. So, the difference of the samples is 10 points. That is your statistic. 10 points. You now have to add on a margin of error, let’s say.. 4. so, youll say something like “I’m 90 % confident that math teachers score between 6 and 14 points higher on IQ tests.”

Question 26

What is a t-crit?

Answer 26

It is the same as z crit. It is the number of sd you reach out in your CI.

To find it, do INVT(area in one tail, degrees of freedom)

Question 27

What is the normal enough condition?

Answer 27

for smaller sample sizes, it must be plausible that the sample may have kind of come from a normalish population.

Question 28

When do you use 1 prop z test instead of one prop t test?

Answer 28

There is no 1 prop t test. You use Z for props. T for means.

Question 29

when is data “paired”

Answer 29

when you have 2 measurements on the same subject (or matched subjects). Often Before-After

Question 30

who invented the t model?

Answer 30

Bill Gosset, guiness brewing company.

Question 31

xbar and mu in t-test?

Answer 31

xbar is your sample mean, mu is yor hypothesized population mean

Question 32

Do you use p-hat or p-null when you calculate your standard deviation?

Answer 32

use p-null..

Question 33

Where did the s.d. of differences ofmeans that is on the formula sheet come from?

Answer 33

Combining models. From the square root of the added variances of the the sampling distributions of the 2 means

Question 34

calc function for: 1 sample mean t test

Answer 34

T Test

Question 35

calc function for: 1 sample mean t interval

Answer 35

T Int

Question 36

calc function for: 1 sample proportion Z test

Answer 36

1-prop Z test

Question 37

calc function for: 1 sample proportion Z interval

Answer 37

1-prop Z int

Question 38

calc function for: 2 sample mean T test

Answer 38

2 samp T test

Question 39

calc function for: 2 sample mean T interval

Answer 39

2 samp T int

Question 40

calc function for: 2 sample proportion Z test

Answer 40

2 prop Z test

Question 41

calc function for: 2 sample proportion Z interval

Answer 41

2 prop Z int

Question 42

calc function for: Paired T test

Answer 42

T test (on L3)

Question 43

calc function for: Paired T Inteval

Answer 43

T int (on L3)

Question 44

What is the T or Z score you get when your are doing a hypothesis test called?

Answer 44

TEST STATISTIC

Question 45

What is the T or Z score you get when doing a confidence interval called?

Answer 45

Z crit (critical Z)

or

T crit (critical T)

Question 46

When can you use Z with means?

Answer 46

Never in inference. You can only use Z if you have the population variance or standard deviation. This only happens in probability problems involving sampling distributions. When we do inference, we don’t know the populuation SD so we use T models. (if we had the population SD, we would also have to have the population mean to calculate it. there would be no reason to do inference if we had that information :) )

Question 47

what is a test statistic?

Answer 47

The Z, the T or the Chi Squared statistic you get in hypothesis testing.

(you put them into normcdf, tcdf, or X₂cdf, respectively)

Question 48

What is a 2 prop Z interval trying to do?

Answer 48

Trying to catch the true difference between the percents of two groups. Like “what is the true difference between the percent of freshmen and the percent of seniors that eat raw cranberries?”