chapter 7: single sample t test

Critical value is based on

degrees of freedom N-1

3. normality

dependent variable is normally distributed in the population - robust to violations of the sample is large

^ What is different about the t distribution, compared to the z distribution?

the shape of the t distribution changes based on the sample size.

3. List the null and alternative Hypothesis

- determined whether it is two tailed or one tailed. one-tailed: use inequalities two-tailed: use equal signs

4. set the decisions rule

- value of t is used to determine whether null is rejected or not - designates the "rare" and "common" zones in the t distribution - abbreviated tcv

^ What are the three pieces of information you need to find the critical t value?

1. is the test one-tailed or two-tailed ? 2. how willing are you to make a type 1 error ? 3. what is the sample size ?

What information will be used for a t test?

1. population mean 2. sample mean (M) & standard deviation (s) 3. critical t value 4. obtained t value

a single sample t test is used to compare:

a sample mean to a population mean when the population standard deviation is not known

2. independence of observations

cases within the sample don't influence each other - not robust to violations

1. Pick the right test. Why does a single sample t test work for this scenario?

comparing a mean of a sample to the mean of a population. we do not know the population standard deviation, so we must choose the single-sample t test.

^

if observed t value falls in the rare zone, null hypothesis is rejected; fail to reject it if it falls in the common zone larger rare zones is for one-tailed test, making it easier to reject the null hypothesis

1. random sample

random sample form the population - robust is violated

^

small sample- more variability, more samples have means that fall further out of a tail, tav falls from midpoint when the same size is small

How does a single sample t test differ from a single sample z test

t test: a sample mean to a population mean when the population standard deviation is not known z test: used to compare a sample mean to a population mean when the population standard deviation is known

t test equation

t=M-U/Sm

2. Check the assumptions. the assumptions for a single t test are:

there are 3.. below