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 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

characteristics of sampling distribution of the mean

conceptual distribution

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

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

sampling error

why is standard “error" instead of SD used to describe variability in sampling distribution of the mean?

because the variability in sampling distribution of the mean is the average deviation of a sample mean from the population mean (whereas in Standard deviation=the average deviation/variability of scores for a variable)

sampling distribution of the mean in simpler words

the distribution of a bunch of sample means

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 determine the probability of any particular sample mean ?????

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

to identify the critical value

What is alpha

the probability of the statistic needed to reject null hypothesis (traditionally set at 0.05)

what does alpha of 0.05 mean

teh null hypothesis is rejected when the p

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

when it is a 2 tail test, the region of rejection is __

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?

1. To compare sample and population mean

2. 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

Mew X bar

The average deviation of the sample mean from population mean

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)

We reject the null! Aka there is a difference btw the sample mean and the population mean

What do we need to mention about inferential statistics

Z statistic and P statement

Assumption of z test for one mean

1. we use random sampling to get our data (equal probability for anyone in the population to be selected in the sample)

2. Must be interval/ ratio level of measurement

3. Data has to be normally 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 standard deviation

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

Mean =0

SD is different (standard has 1 SD only)

Mean of T distribution

0

How does T distribution shape change with sample size

Approximately normal, but 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 fed to vary when using a sample statistic to estimate a population parameter

If you can’t find the exact cv on table, you pick__

Conservative, further away from center of distribution