Sampling Distribution of a Difference Between Two Means

What conditions must you check when constructing a confidence interval for Sampling Distribution of a Difference Between Two Means

10%, random, and large counts *be sure to check for everything and use proper notation

What do you say for the type of interval test?

two sample t interval for μ1 - μ2

What type of interval is it?

two sample t interval for μ1 - μ2

What type of test do you do for significance testing of difference of means?

two sample t test for μ1 - μ2

Two sample t procedures vs paired t test

two sample t test: if groups were formed using completely randomized design paired t test: if subjects were paired and the split at random into the two treatment groups of if each subject received both treatments or if random sampling has occurred with two statistics are taken from a single subject for comparison

Shape of Sampling Distribution of a Difference Between Two Means

when populations are Normal, the sampling distribution of x bar1 - x bar 2 is approximately normal *can check conditions like graph if small sample or > 30

For an interval, what t value do you use?

you can use the one you get by doing the smaller of n-1 and then calculate the interval by hand or the one produced by the calculator using the df it gives you *either way, you must stay consistent

*make sure to show your df, even if from the calculator

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*make sure to use the word "independent" in random condition

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How do you properly design an experiment?

- hat method, detail which group you are assigning to which treatment or how you will assign to treatments, compare scores (if test)

What is the state for creating a two sample t interval?

We want to estimate μ1 - μ2 at the c% confidence level where, (define variables)

What do you put in the state for a significance test of difference of two means?

We want to perform a test of (hypothesese) where, define variables and state significance level

What are the null hypotheses for mean?

all are the same as the ones for proportions, just using μ instead

How do you interpret p value?

assuming the null is true, there is a____________ probability of getting a. mean difference (context and show subtraction) by chance alone/random assignment

What way can you find df and what must you know about it?

calculator, use the smaller of the n1 -1 and n2 - 1

If the data is small what must you do, what do you say, what must you rememebr?

check graphs, label graph, if now skewness or outliers, state so and proceed with t procedures, we can assume μ - μ distribution is approximately normal

Where t* is the

critical value with c% of its area between -t* and t* for the distribution with degrees of freedom

For a difference in mean, when does an interval not provide convincing evidence that their is a difference?

if the interval contains 0

What word must you include in your random condition for a two sample test

independent

How do you find t*?

invt, carful with area (use the left tail area)

Why do you use the smaller df?

its the conservative approach, larger df is closer to normal, safer (worst case senario)

If a value is closer to the null, it has

lower power

center of Sampling Distribution of a Difference Between Two Means

mean of sampling distribution is μ1 - μ2

Remember if you have not equal to, what must you differently?

multiply by 2

spread of Sampling Distribution of a Difference Between Two Means

standard deviation can be found by adding as long as each sample is no more than 10% of its population *must check 10% condition!

What is the critical value?

t*

*must still show work for p value, use

tcdf

When you check your random condition, what must you be careful to state?

that the data come from random experiments