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2023 MIDTERM REVIEW > UNIT 5, 6, 7 part A > Flashcards

UNIT 5, 6, 7 part A Flashcards

1
Q

What is a test statistic?

A

It is a z score- It is the number of SE your statistic is away from the null parameter.

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2
Q

what is a p-value

A

At the end of a hypothesis test, it is the likelihood of getting your results if the null was true.
normcdf ( test stat, 999 )

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3
Q

notation: what is z*

A

critical z, how many SE you are reaching up and down in a confidence interval for proportions

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4
Q

notation: what is Ho

A

The NULL, the dull, the “things haven’t changed” hypothesis

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5
Q

notation: What is Ha

A

The alternative. This is what you are trying to prove.

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6
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.

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7
Q

What is a sampLING distribution?

A

a pile of statistics. A pile of p-hats or x-bars.

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8
Q

Are models what really happen?

A

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

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9
Q

If the null parameter is in your confidence interval, can you reject it?

A

No. It is still plausible.

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10
Q

What is “statistically significant?”

A

When our sample statistic is so far away from what we were expecting that we don’t think that it was due to random sampling error. Then is statistically significant. When p-value is below the alpha, we say “statistically significant”.. Low p-values are statistically significant.

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11
Q

What is the difference between standard error and standard deviation?

A

Standard error is the typical distance a STATISTIC is from the mean in a sampling distribution (pile of a bunch of sample’s statistics) and Standard DEVIATION is the typical distance a DATUM is from the mean in a pile of raw data.

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12
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)

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13
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) )

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14
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!)

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15
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)

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16
Q

What happens to a pile of statistics if you take larger samples?

A

All of the x-bars or all of the p-hats will get closer to each other, and closer to the parameter ( mu or p). There is less variability in the sampling distribution (in the pile of stats).

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17
Q

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

A

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

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18
Q

N (12, 22 )
What does this mean?

A

it means NORMAL models centered at 12 With a standard deviation of 22

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19
Q

Consider the distribution of a sample compared to the distribution of the population.

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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20
Q

What is a standard error?

A

The typical, or expected, error. It is how far off you are expecting your statistic to be from the parameter. 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

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21
Q

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

A

Larger sample statistics have less variablility, so statistics from larger samples are closer to eachother and to the parameter. Statistics from smaller samples are more spread out, further away from true parameter.

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22
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.

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23
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…

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24
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

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25
Q

What is the Fundemental Theorem of Statistics?

A

The CLT!! The Central Limit Theorem!
Piles of x-bars are approximately normal even if the population is skewed or bimodal when n>30!

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26
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!

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27
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!!!

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28
Q

What is a point estimate?

A

Your statistic. It is the best “one - number” guess at the parameter.

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29
Q

What is a biased estimator? Give an example

A

When the pile of statistics is not centered on the true parameter (p-hats not centered at p, or x-bars not centered at mu).
If you are looking for the average time high school students can hold their breath, and you only take samples with kids from swim teams, your pile of x-bars will be centered higher than the true mu because swimmers can hold their breath longer. Biased sampling methods give biased estimators.

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30
Q

What is an unbiased estimator?

A

When the sampling distribution (pile of sample stats) is centered on the true population parameter. Good sampling methods should give unbiased estimators.
It is unbiased if the pile of p-hats is centered at p, or if the pile of x-bars is centered at mu.

31
Q

what is a biased estimator?

A

When the sampling distribution (pile of sample stats) is NOT centered on the true population parameter. A pile of p-hats not centered at p, or a pile of x-bars not centered at mu.
Suppose you were weighing people and there was a 1 pound weight on the scale, the pile would be centered 1 pound higher than mu. Baised.

32
Q

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

A

mean is mu and standard deviation is sigma/root n (look at formula sheet) N(mu, sigma/rootn)

33
Q

What if you want more confidence?

A

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

34
Q

when do you need crits?

A

in confidence intervals
STAT +/- CRIT (SE)

35
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.

36
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.

37
Q

What is a critical value?

A

It is the amount of standard errors you’ll reach out, depending on your confidence. Example..
68% crit z = 1 ..
95% crit z = 2
99.7 crit z = 3

38
Q

What is a Z* ?

A

It is a z-crit. (I know a little z-crit)
about 2 for 95% intervals
about 3 for 99.7% intervals

INVNORM(area 1 tail)

39
Q

what does “95% confidence” in a 95% confidence interval mean? (explain the confidence level)

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.

40
Q

Do parameters vary?

A

NO!!! Statistics do because they are calculated from samples, different samples have different statistics. they vary from sample to sample. The parameter doesn’t vary because there is only one.

41
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)

42
Q

What is a confidence interval?
How can you think of it?

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)

43
Q

Can you make a 100% confidence interval?

A

Sure, I’m 100% confident that it will snow between 0 and 500 feet tomorrow.
So wide it gives really no info.

44
Q

Is a confidence interval a PROBABLILITY?

A

NO.
It is saying that if you made a bunch of them, then 95% would catch the truth.

45
Q

What are we confident in?

A

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

46
Q

Will 95% of other statistics be within my interval?

A

NO!!! You have no idea where your statistic is (or your interval) in regards to true parameter

47
Q

What if you want more cofidence with same size interval?

A

increase your sample size

48
Q

How is a margin of error different from a standard error?

A

A margin of error is a NUMBER OF STANDARD ERRORS. It is how far up or down you go in a confidence interval. A standard error tells you about the spread of a pile of statistics (a sampling distribution).

49
Q

What is a point estimate?

A

Your p-hat or your x-bar. Your best guess. What you got in your sample. It is in the middle of the interval.

50
Q

How do you find Margin of Error from an inteval? Like (.35, ,45)

A

It is half the width.. (HI-LO divided by 2)
So in this case, the ME is .05
Remember you stand at statistic (point estimate) and reach up and down a Margin of Error. So an inteval is always exactly 2 margins of error wide)

51
Q

How do you find point estimate from an interval? like (.35, .45)

A

It is the STATISTIC, it is in the dead center of interval. so take the average of the upper and lower bounds. In this case it would be at .40.

52
Q

interpret this 90% confidence interval for avg weight of mice (2.3, 3.5) in ounces

A

I am 90% confident that the mean weight of mice is between 2.3 and 3.5 ounces

53
Q

what does “ 90% confidence” mean in a 90% interval for avg weight of mice (2.3, 3.5) in ounces

A

90% of intervals made this way would catch the true mean weight. If you took 100 samples and made 100 intervals, about 90 intervals would catch the true weight, about 10 would not.

54
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”

55
Q

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

A

set alpha= .02 and reject only p-values below that

56
Q

what is another name for alpha level?

A

a significance level

57
Q

How do you write conclusion if you reject?

A

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

58
Q

How do you write conclusion if you fail to reject?

A

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

59
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.

60
Q

What is the NULL HYPOTHESIS?

A

The DULL HYPOTHESIS, the nothing changed hypothesis, the no-difference hypothesis, the “he’s telling the truth” hypothesis, the “No trickery” hypothesis

61
Q

Which hypothesis shows what you are trying to prove?

A

The alternative.

62
Q

If the p-value is low, (below alpha), how do you write conclusion?

A

With p-value this low (show p value < alpha) I reject the null hypothesis. There is strong evidence that the proportion of students who eat rice has changed.

63
Q

If the p-value is high, (above alpha), how do you write conclusion?

A

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

64
Q

you reject when _____________ evidence

A

you reject when YOU HAVE EVIDENCE

65
Q

you fail to reject when ____________ evidence

A

you fail to reject when you FAIL TO HAVE EVIDENCE

66
Q

Can you “accept the null?”

A

No! we don’t accept the Ho. We just fail to reject.

67
Q

In order to reject a null hypothesis, you need ___________

A

evidence

68
Q

Can you prove a null hypothesis true?

A

NO.. We just fail to reject it.

69
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
70
Q

what is a test statistic?

A

number of SE away from the null parameter.

(STAT-PARAMETER)/SE

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

71
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. A pile of p-hats or x-bars.

72
Q

What is alpha?

A

It is the rejection area. Generally, we use .05. The significance level.

73
Q

If you have a test statistic and need a p-value, what can you do?

A

If Ha>NULL
NORMCDF(test stat, 999)
if Ha< NULL
NORMCDF(-999, test stat)

74
Q

What do we compare our p value to in a hypothesis test?

A

compare it to alpha. if p value is below alpha, reject. Above alpha, fail to reject.

2023 MIDTERM REVIEW (6 decks)

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