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2015 AP STATS > UNIT 5 > Flashcards

UNIT 5 Flashcards

1
Q
A
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2
Q

Are models what really happens?

A

No. A model train is not a real train. We use models to say what kind of happens.

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3
Q

Can you accept a null hypothesis? Can you say “keep the null?”

A

Never accept a Ho, don’t keep the Null. simply “FAIL TO REJECT THE NULL”

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4
Q

Can you decrease alpha while increasing power (even though they move together?)..

A

Yes.. They move together with constant sample size. If you increase the sample size, you can decrease alpha and increase the power.

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5
Q

Can you draw the alpha/beta/power diagram?

A

See page 486. Be able to draw and label this the way we do in class with the box and “RETAIN REJECT” up top and “Ho TRUE, Ho FALSE” on left.

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6
Q

Can you make a 100% confidence interval?

A

Sure, I’m 100% confident that it will snow between 0 and 500 feet tomorrow?

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7
Q

What is sample size formula for proportions?

A

n= (z^2 * p * q )/ (ME ^2)

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8
Q

Can you prove a null hypothesis true?

A

NO.. We just fail to reject it

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9
Q

Describe the distribution of a sample

A

It will look like the population. The distribution of a sample is a histogram made from the sample, which will look kind of like the population. If the population is bimodal, then the distribution of the sample is bimodal. The SAMPLING distribution of a bunch of means, however, will look normalish.

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10
Q

Do parameters vary?

A

NO!!! Statistics de. they vary from sample to sample. PARAMETERS DO NOT VARY!

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11
Q

What does a “significance level of .02” mean?

A

set alpha= .02 and reject only below that

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12
Q

If you are doing a 2 tailed test with alpha=.05.. What confidence interval goes with that?

A

95% confidence interval (there is .025 in each tail)

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13
Q

If you are doing a 1 tailed test with alpha=.05.. What confidence interval goes with that?

A

90% confidence interval (there is .05 in ONE tail)

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14
Q

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

A

use p-null..

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15
Q

Do you use p-hat or p-null when you check the success/failure condition?

A

use p null

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16
Q

How do you pool with 2 proportions?

A

COMBINE HANDFULS: (X + X) / (N + N)

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17
Q

how are alpha and beta related?

A

as one increases, the other decreases, and vice versa

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18
Q

how are beta and power related

A

as one increases, the other decreases, and vice versa. They have to because they BOTH ADD TO ONE!!! Power + Beta = 1

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19
Q

How are power and alpha related?

A

they go up and down together

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20
Q

How can you decrease alpha and beta at the same time?

A

increase sample size. this will also increase power.

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21
Q

How can you increase power?

A

Increase alpha or increase sample size..

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22
Q

How do statistics from big samples compare to small? (notice this doesn’t ask about DATA)

A

Larger sample statistics have less variablility, so statistics from them are closer to the parameter and eachother. Statistics from smaller samples are more likely to be far away from true parameter.

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23
Q

How do you write conclusion if you fail to reject?

A

With a p-value this high. I fail to reject the null. There is not enough evidence to say that more students like eggs now.

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24
Q

How do you write conclusion if you reject?

A

With such a low p-value, I reject the null hypothesis. There is strong evidence that the proportion of students who eat rice has changed.

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25
Q

How else can you explain power?

A

The likelihood you correctly reject a false null.. The likelihood you correctly detect what you were trying to detect

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26
Q

How can you think of TYPE 2 error?

A

the missed opportunity error.. You failed to see an effect

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27
Q

How is a confidence interval made?

A

statistic +- margin of error. Statistic +- (crit * s.d ). Stand at the statistic, reach out up and down a margin of error, and hope that you catch the parameter.

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28
Q

How wide is a confidence interval? (how many ME?)

A

It is 2 margins of error wide ALWAYS (DON’T CONFUSE WITH NUMBER OF SE)

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29
Q

If the null is false, what is the only error you could make?

A

Type 2

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30
Q

If the null is true, what is the only error you could make?

A

Type 1

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31
Q

If you fail to reject, what is the only type of error you could make?

A

Type 2

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32
Q

If you reject, what is the only type of error you could make?

A

Type 1

33
Q

N ( ?1 , ?2 ) what does this mean?

A

it means NORMAL models centered at ?1 With a standard deviation of ?2

34
Q

One tail or 2 tailed? How do you tell?

A

if it just says “changed” or “different”.. Then it is 2 sided.. DOUBLE THE P VALUE!If it says “more” “less than” “greater” etc.. Then it is just one sided..

35
Q

What are conficence intervals for?

A

PARAMETER CATCHERS. They are an attempt to say what the true population parameter is.. It is our best guess. “We think that there will be between 8 and 12 inches of snow”

36
Q

What are the 3 steps in hypothesis testing AFTER YOU CHECK CONDITIONS?

A
  1. Make your Ho and Ha 2. Make a Null Model (centered at null, use your Ho as center and in calculations, use your sample size).. This is a sampling distribution for the statistics if the null were true. 3. THINK then CHECK. use your statistic (p-hat, x-bar, phat1-phat2, xbar1-xbar2) to calculate your test statistic and then p value
37
Q

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)..

A
  1. Randomization (this helps with assumption of independence 2. SMALL ENOUGH SAMPLE … 10% condition (this is the upper limit of our sample size. above this, the sampling distribution starts looking leptokurtic (thinner and taller), not normal)3. LARGE ENOUGH SAMPLE.. success/failure: np and nq > 10. this is the lower limit of our sample size. It is when the sampling distribution starts looking normal. FOR 2 SAMPLES YOU NEED BOTH SAMPLES TO MEET THESE REQUIREMENTS!
38
Q

What are the mean and standard deviation of a sampling distribution for a proportion?

A

mean is p and sdandard deviation is root pq/n (look at formula sheet) N(p, root (pq/n) )

39
Q

What are we confident in?

A

our confidence lies in our interval. if we took another sample.. We’d have a different interval..

40
Q

what does 95% confidence interval mean?

A

It means if we took a ton of samples, and made confidence intervals from each of them,ABOUT 95% of the intervals would contain the parameter, 5% would not.

41
Q

What does Central Limit Theorem Say?

A

It basically says.. NO MATTER WHAT SHAPE THE POPULATION IS (normal, bimodal, uniform, skewed, crazy.. ) If you make a histogram of a bunch of means taken from a bunch of samples, that histogram will be unimodal and symmetric WITH LARGE ENOUGH SAMPLES.. Close to normal. So.. A nerdy way to say it is: The sampling distribution of means is approximately normal no matter what the population is shaped like. The larger the sample size, the closer to normal. (the normal curve is just a model.. the sampling distribution is close to it, but not it! we use the model anyway!)

42
Q

What does the CLT say about the distribution of actual sample data?

A

Nothing? The sample will be distributed similar to the population. The CLT only talks about distributions (histograms) of sample statistics, which are groups of means.., NOT OF INDIVIDUALS!!!! NOT DATA

43
Q

What does CLT say about the distribution of the population?

A

Not much… just that it doesn’t matter what it is.. With large samples.. The SAMPLING dist will be approx normal (dist of stats.. NOT DATA)

44
Q

What if you want more cofidence with same size interval?

A

increase your sample size

45
Q

What if you want more confidence?

A

get a bigger net.. (wider conficence interval) (or increase sample size)

46
Q

What is “statistically significant?”

A

When p-value is below the alpha, we say “statistically significant”.. Low p-values are statistically significant. When our sample most likely didn’t happen randomly, that is statistically significant.

47
Q

What is a confidence interval?

A

it is a parameter catcher.. Like a fishing net. We stand at our statistic, and reach up and down a margin of error, and hope to CATCH the parameter? sometimes we do, sometimes we don’t? but we never know.. Mooo hooo hooo haaaa haaa haaa (evil laugh)

48
Q

What is a critical value?

A

It is the amount of standard deviations (errors) you’ll reach out, depending on your confidence (a t or z). Example.. 68% crit z = 1 .. For 95% crit z = 2 (well, 1.96).. For means.. Use t crits

49
Q

What is a margin of error?

A

critical * s.d. It is how far you reach out in a confidence interval.. You reach up and down one of these, so the interval is actually 2 margins of error wide.

50
Q

What is a null model?

A

It is a sampling distribution. It tells us how sample statistics would vary if the null were true. It is centered at the null.

51
Q

what is a parameter?

A

some numerical summary of a population. Often called “the parameter of interest.” It is what we are often trying to find.. It doesn’t vary. It is out there and STUCK at some value, it is the truth, and you’ll probably not ever know it! We try to catch them in our confidence intervals, but sometimes we don’t (and we don’t know it!). It Could be the mean of a population, the standard deviation of a population, the proportion of successes in a population, the slope calculated from a population, a difference of 2 means from 2 population, a difference of 2 proportions from population

52
Q

What is a p-value

A

It is the probability of getting your sample randomly if the null were true. Basically, how likely is it that your sample statistic came from the Null Model.

53
Q

What is a standard error?

A

It is calculated like the standard deviation, but we are using sample statistics.. We don’t know the true parameters, so we estimate with statistics adding error to our calculation

54
Q

what is a statistic

A

some numerical summary of a sample.. Could be the mean of a sample, the standard deviation of a sample, the proportion of successes in a sample, the slope calculated from a sample, a difference of 2 means from 2 samples, a difference of 2 proportions from 2 samples, a difference of 2 slopes from 2 samples.. you can make sampling distributions for any of these, and they will all be centered around the parameter…

55
Q

what is a test statistic?

A

a t or z score (or chi squared) that you use to find a p value

56
Q

What is alpha?

A

It is the rejection threshold. You reject p-values below it.. It is how willing you are to make a Type 1 error? alpa=P(Type I error)

57
Q

What is beta?

A

It is probability that you’ll make a Type II error.. P(Type II error)

58
Q

what is difference between assumptions and conditions?

A

Assumptions must be made in order to perform inference. We need to assume independent sample values and a large enough sample (but not too large). We check conditions to help support our assumptions.

59
Q

What is effect size?

A

Difference between null and true parameter. something we don’t know

60
Q

What is power?

A

The probability that you correctly rejected a false null

61
Q

What is sampling error?

A

same as sampling variability.. The natural variability between STATISTICS.. NOT DATA!!! . We call it error EVEN THOUGH YOU MADE NO MISTAKES!!!

62
Q

What is sampling variability?

A

same as sampling error. The natural variation of sample statistics.. NOT DATA.. Samples vary. so do their statistics.. Parameters do not vary!

63
Q

What is statistical inference?

A

Using a statistic to infer something about a parameter.. Basically, using a sample to say something about a population.

64
Q

What is the difference between the distribution of a sample and a sampling distribution?

A

A distribution of a sample is just a histogram of the DATA in a sample. A sampling distribution is made from an bunch of sample STATISTICS. It is the distribution of the statistic that was calculated from those many many samples.

65
Q

What is the Fundemental Theorem of Statistics?

A

The CLT!! The Central Limit Theorem!

66
Q

What is Type 1 error?

A

We reject when we shouldn’t have (the null was actually true)

67
Q

What is Type 2 error?

A

We fail to reject when we should have rejected (the null was actually false)

68
Q

When we are looking at differences of proportions, what is the sampling distribution a distribution of?

A

A PILE OF DIFFERENCES (p hat - p hat). You have to imagine taking a a pair of samples, say.. Of girls and boys, subtracting phat girl-phat boy, and then writing that difference down. Do this over and over again, and you will have a list of differences. Now make a histogram of that list of differences, and that is your sampling distribution. It is an imagined distribution of an infinite amount of differences (of sample pairs)..

69
Q

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

A

pythag of stats.. Adding variances! From the square root of the added variances of the the sampling distributions of the 2 proportions

70
Q

How do you POOL with MEANS?

A

YOU DON’T

71
Q

How do you POOL with PROPORTIONS?

A

You combine the two samples into one big sample. TOTAL # RED BEADS / OVERALL TOTAL OF ALL BEADS

72
Q

Will 95% of other statistics be within my interval?

A

NO!!! You have no idea where your interval is in regards to true parameter

73
Q

Is a confidence interval a PROBABLILTY?

A

NO

74
Q

What is difference between population of interest and parameter of interest?

A

Population is the WHO (subjects you measure, beads people) Parameter is the actual number you want (like % of or AVG)

75
Q

What does PHANTOMSA stand for?

A

Parameter, Hypothesis, Assumptions, Name the test, Test Statistic, Obtain P VALUE, Make Decision, State conclusion in context, ANSWER QUESTION

76
Q

What does PANICA stand for?

A

Parameter, Assumptions, Name the test, Interval, Conclusion in context, Answer the question

77
Q

how do you find z and t crit?

A

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

78
Q

when do you need crits?

A

in confidence intervals (and old fashioned hyp tests.. We look at Z to see if greater than crit.)

2015 AP STATS (11 decks)

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