STATS

Examples of circumstances where standard deviation is known.

Standardized tests-IQ or college entrance exams

greater sample sizes give us a ___ view of the population

better +samples will be more consistent and more accurate +the many samples will not be as varied +most sample means are close to the population mean +the mean of the sampling distributions is the same as the mean of the population

State hypothesis ____ (before or after) you find your results or look at your data

before

For the single-sample t test the confidence interval ...

calculates the range for how big the difference is between two population means

As sample size increases, the confidence interval becomes _____ and _____ precise.

larger, less

we are searching for how unlikely our alternative hypothesis is if we assume that the null is correct.

the basic of null hypothesis testing

Z-values are used when..

the standard deviation is known

T-values are used when...

the standard deviation is not known +more common

null hypothesis states

there is no relationship

Smaller sample size ____ the sampling error

increases

What does sample error tell us?

How well the sample mean reflects the population mean

Uniform Distribution

Distribution where populations are spaced evenly, each variable has the same probability

An example of Uniform distribution

Rolling dice

An example of Continuous distribution

Sum of two dice

Why do we need sampling distributions?

Tells us how representative a sample is of the population.

Standard deviation

Tells us how well the mean represents the sample data

Significance Testing

Testing to determine the probability of there being a "true" difference between scores of a data set. Involves testing a null hypothesis in order to prove it, and therefore disprove the difference. determines whether the observed difference was likely to be created by sampling error

Trade off between Type 1 and Type 2

The bigger the tails the more Type 1 error The smaller the tails the more Type 2 error Find a balance

Computing the level of confidence you need what three things

The point estimate The critical value from the t table for the CI The expected sampling error

continuous distribution

The probability of obtaining a value is always zero

Statistical significance with the type of errors

Type 1: We reject the null but the null is actually correct Type 2: We fail to reject the null but the null is actually incorrect

Why do we care about the area under the curve?

We can tell how likely a given value is , we decide what range of values we should expect to see by chance

sampling distribution show us what about the null hypothesis?

What we should expect if the null were true

How can you prove a null hypothesis?

You can't. But you can disprove one.

Central Limit Theorem

as sample size increases, the distribution of sample means of size n approaches a normal distribution. Larger samples: sampling distributions will be normally-distributed, closer to the normal curve. The mean of the sampling distribution will equal the mean of the population. You can calculate the standard deviation.

The critical value for a two-tailed t test with α = .05...

changes based on sample size

SE x

estimated standard error

the absence of evidence is not ..

evidence of absence

As sample size increase the critical value ...

gets smaller (less extreme)

effect size

helps a researcher to determine whether an effect is large enough to be useful.

The relationship between confidence level and interval width is such that as our confidence increases (from 95% to 99%, for example), the estimate will be come _____ precise.

less

The wider of Confidence Interval the ____precise our estimate of our population is

less

The population can be bimodal, the distribution can be bimodal but using the CLT, we know that the sampling distribution will be..

normal

point estimate vs interval estimate

point estimate: ((sample mean)), single most plausible/reasonable value interval estimate: ((upper and lower boundaries)) determines the range of other plausible values

Large sample size ___ the sampling error

reduces

The probability of committing a Type 1 error ...

same as the alpha ex. alpha=.05 so Type 1 error = 5% chance of error ex. alpha= .01 so Type 2 error= 1% chance of error

The ____ provides an average of how far different sample standard deviations deviate from the true mean

sample error

To construct a confidence interval of the mean a value is added and subtracted from the _____

sample mean

Samples from a population are also called

sampling variation

If we want to estimate the population parameter we use

standard error

ox =

standard error

Assume alpha is 0.05 As a sample size increases the rare zone (critical region) ...

stays the same size (equal to 5%)

use ____ values when the standard deviation is unknown

t

we fail to reject the null when___

t values fall in between the common zone

we reject the null when ___

t values fall in the rare zone

sampling distribution

the distribution of values taken by the statistic in all possible samples of the same size from the same population. the distribution of a bunch of sample means

How is the size of the interval around the sample mean is determined

the expected amount of sampling error the level of confidence (95% or 99%)

Confidence Intervals

the range on either side of an estimate that is likely to contain the true value for the whole population estimates a population parameter with a specific level of confidence and precision

we're working with ___-tailed t tests

two

more confidence = ____ margin or error

wider

If you conclude there isn't enough evidence to reject the null ....

you fail to reject the null

use ____ values when the standard deviation (sigma) is known

z

a ____ is a point along the baseline of a normal curve

z-score/value