206 7-testing one sample mean

A type 1 error occurs when researchers concludes based on their ____, that an effect ___ when it actually occur in the

sample data, that an effect exist when it actually does NOT occur in the population

type 1 error occurs due to ___

Sampling error

What's the symbolizes the probability of making a type 1 error

Alpha

When do we define the probability of making a type one error

Beginning of the study

false positive aka type ___ error

I

false negative aka type ___ error

II

how does type 1 error influence null hypothesis

type 1 error falsely rejects the null hypothesis whenwe shouldn't have rejected the null in population

when testing one sample mean, we wanted to know if the ____ is actually equal to the ____

sample mean

sampling distribution of the mean is a conceptual/frequency distribution

conceptual (based of an infinite set of numbers)

symmetry, modality, and variability of sampling distribution of the mean

symmetrical (normally distributed, bell shape)

unimodal (mew= population mean)

variability= standard error of the mean

mean of sampling distribution of the mean =

population mean (mew)

standard deviation vs standard error

SD= average deviation of a score from mean of a variable

SE= average deviation of a sample mean from population mean

Standard Error of the mean vs population standard error of the mean both calculate ___

however, you use SEM in ___test, where ___unknown/known

you use PSEM in ___, where ___unknown/known?

Both calculates the average deviation of sample mean from population mean

Sxˉ (SEM)= when population SD is UNknown, used in T-test

σ_x- (PSEM)= when population SD is know, used in Z-test

why is it unlikely that sample mean would exactly equal to population mean

sampling error

why do we use standard “error" instead of SD  to describe variability in sampling distribution of the mean?

bc SD is the average deviation of a score from its mean, but in sampling distribution of the mean, the average deviation of a score from its mean= average deviation of a sample mean from the population mean

“distribution of statistics for samples randomly drown from population”

= sampling distribution

sampling distribution of the mean in simpler words

the distribution of a ton of means randomly drawn from the population

how to make a sampling distribution of the mean

randomly select a sample size of N from the population, get the mean of the sample, repeat

why is it important that sampling distribution of the mean is normally distributed

this allows researchers to mathematically determine the probability of any particular sample mean (inferential statistics like Z-test and T-test assume that distribution of sample is normal)

4 steps of testing one sample mean

1. state null and alternative hypothesis

2. make a decision about the null hypothesis (set alpha)

3. draw conclusion from analysis

4. relate result of analysis to research hypothesis

why do we set Alpha

to decide the threshold of statistical significance (aka critical value)

alpha is the level of ___ needed to ___

statistical significance

reject null hypothesis 

what does alpha of 0.05 mean

the null hypothesis is rejected when the p>0.05

why do we refer to the scores of standard normal distribution as z-statistic rather than z-score

because we are using this distribution to calculate a statistic that tests the difference btw a sample mean and a population mean (aka SD of sample mean from population mean), not just btw score and its mean

when it is a 2 tail test, alpha is ____ regions of rejection

split into 2 half (0.025+0.025)

How to get critical value in one test

Find the region or rejection’s corresponding z-statistic

ones we determined the critical values (ex: +- 1.96), we can set the decision rule:

if z < -1.96 or z> 1.96, reject null hypothesis; otherwise, do not reject null  (aka if the sample mean falls in these 2 regions of rejection, it means that the statistic have a low probability of occuring

When do we do a z test for one sample mean?

To compare sample and population mean + population standard deviation is known

What’s in the numerator is what we’re testing, so in the z-statistic formula the numerator is__

Sample mean - hypothesized population mean

population standard error of the mean (σxbar)=

The average deviation of the sample mean from population mean (known)

z statistic= what divided by what

(sample mean-hypothesized pop mean) / pop standard error of mean (PSEM)

What does it mean that the standard error of the mean = 0.21 sec mean (flex arm hang

The average deviation of sample mean from population mean is 0.21 sec

What does it mean if you obtain a z- statistic of 4.76 mean? (If your critical value is +-1.96)

there is a statistically significant difference btw the sample mean and the population mean, so we reject the null

when drawing conclusion, what do we need to mention about inferential statistics of a Z-test

Z-statistic and P statement 

which is the descriptive statistics of the variable

M=8 sec

μ=7 sec

“the sample is statistically significantly greater than the population“ stated what component of a conclusion

nature and direction of finding

Assumption of z test for one mean

1. random sampling

2. Must be interval/ ratio level of measurement

3. normality of dependent variability distributed shape (Unimodal, symmetrical, mesokurtic)

How to tell if a distribution is unimodal

Look at histogram

How to tell if distribution is symmetrical

Skewness statistics

relationship btw mean & median

Look at histogram

How to tell if a distribution is mesokurtic

Kurtosis statistics

Why do we do a T test for one sample mean

We also wanna know the difference btw sample mean n hypothesized population mean, BUT we don’t know the population SD

When should we use T test instead of z test

When pop SD is unknown

Similarity and differences btw T distribution and standard normal distribution (aka Z distribution)

Mean =0

SD is different (Z’s SD is always 1)

Mean of T distribution

0

How does T distribution shape change with sample size

Approximately normal, but the shape gets closer to normal distribution as sample size increase

What’s 3 thing u need to read a T table

Alpha, df, one /two tail test

What’s degree of freedom

Number of values that are free to vary when using a sample statistic to estimate a population parameter

If you can’t find the exact cv on table, you pick the one that’s ___ from center of distribution

Conservative, further away from center of distribution

If you increase sample size, this will ___ standard error of the mean and ___ t statistic and critical value get ___ to center of distribution because ___ gets larger

Decrease SEM

Increase T-stat

closer

Degree of freedom

Larger sample size = greater ___ to reject null hypothesis

Probability

How does a larger alpha affect the likelihood of rejecting null hypothesis

CV move towards center of distribution» larger region of rejection» increase probability of falsely rejecting alpha

Why don’t we increase alpha to reject null easier

Bc you would increase your probability of making type 1 error / false positive/ falsely rejecting (what alpha is)

Is it easier/ greater likelihood to reject one tail or two tail

One tail

similarities and differences btw the formula for z-score and z-test for one mean

finding probability of different reasons

both based off standard normal distribution (

proability of a statistic falling in a range

z=(score-mean)/SD =in standard normal distribution, how many SD is the score from the mean (mean=0, SD=1)

z test= (sample mean-hypothesized population mean)/population standard error of the mean = how many PSEM is the sample mean from the hypothesized pop mean (mean of z-test=0, pop mean & pop SD is known)

what 2 factors influence the variability in a distribution of sample mean

SE= pop SD/root

1. pop SD

2. sample size