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What is the Central Limit Theorem?
The Central Limit Theorem states that if the samples are drawn randomly, as sample size increases, the distribution of sample means approaches a normal distribution centered around the mean of the population from which the samples are drawn. From the CLT we get three facts.

The CLT is important because the 3 facts give us the sampling distribution (the distribution resulting from the collection of actual data). what are the 3 facts?
 1. μx sub x bar=μ mean of the population
 2. σx sigma sub x bar= σ standard dev of pop
 =
 √n # of ppl in sample
 ^^ standard of error of the mean standard deviation of this distribution, how SPREAD out the scores are. Tells us how much VARIABILITY we can expect due to random sampling from population. How far from the mean can we expect to find likely sample means.
 3. No matter what the shape of the pop distribution, as the sample size increase, the sampling distribution of sample means approaches a normal distribution.

Why is the CLT important?
It is important because the 3 facts give us the sampling distribution which allows us to test our hypothesis.

What effect does increasing sample size have on the CLT?
Increasing the size of the sample has no effect on the mean of the sampling distribution, but it makes the standard deviation of the sampling distribution smaller. This means it will be easier to find significant difference. Also, an n increases, the sampling distribution approaches normality (n=30)

What is the sample distribution?
Sampling distribution is the probability distribution of the statistic calculated from all possible random samples of the size from the same population.

Why is sampling distribution important?
It is important because it tells us how much we expect two random samples from the sample population will differ just because of chance (individual difference, subject variables). If our differences are greater than we expect from the sampling distribution, then we say it is a REAL difference or a treatment effect.

How do the CLT and the Sampling distribution relate?
They relate because you use the 3 facts of the CLT to get sampling distribution.

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
STEP 1:State the null and alternative hypotheses.
 Step 1. State the null and alternative hypotheses.
 The null hypothesis (Ho) states that the sample was just a random sample from the target population. That is, the population that could have reasonably produced the sample was the target population and as such, the treatment had no effect on this sample.
The null hypothesis attempts to show that no variation exists between variables, or that a single variable is no different than zero. It is presumed to be true until statistical evidence refutes it for an alternative hypothesis.
The alternative hypothesis (H1) states that the treatment effected or changed the sample enough that it is not the same as a random sample from the target population. Instead it is from a different population consistent with your theory.

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
STEP 2:Determine the rejection region by setting alpha
The alpha level provides a cut off separating the sample that are likely random sample from unlikely random samples. If the mean of your treated sample is far enough from the mean of the population then we decide to reject the null hypothesis. Alpha (usually .05 or .01) determines how far that distance must be. If the mean of the sample falls in the rejection region (at or beyond alpha), then we say that it is so different that we do not believe it to be a random sample from this population. We believe that the treatment was effective and this is a sample from a population of treated persons that has a different mean. (NOTE: Drawing the rejection region and labeling it as well as labeling alpha will ensure that Dr. Britt understands your wording)

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Step 3: Specify the test statistic (z,t,F,f,X2) and find the critical value in a table
Step 3: Specify the test statistic (z,t,f,X2) and find the critical value in a table
 draw out tree diagram or use words
 If you have more than one IV, use a two factor ANOVA (F test). With one IV you must determine the number of levels of that IV. IF there is only a single level (one sample), then use a one sample z test (if the population variance O2 is known) or a one sample t test (if pop variance is NOT known). If you have two levels (2 samples) then determine if they are independent (i.e. between subjects)independent t test or dependent (within subjects, matched, correlated, prepost test) dependent t test. Finally if you pne IV and have 3 or more levels, use a one way or one factor ANOVA (f test)

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Step 4: Determine the mean and standard deviation of the sampling distribution or explain how to get sampling distribution.
 Step 4:
 State the mean and variance of the sampling distribution of the mean
 Compute the standard error of the mean
 State the central limit theorem
*see answer...

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Step 5: state it
Step 5: Set up an if then decision rule for stating when to reject Ho. If the observed score is beyond the critical value (in rejection region) then reject Ho and say that the difference is statistically significant at the stated alpha level. In this case the alternative hypothesis is accepted and we say that the treatment was effective.

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Step 6: State it
Calculate the observed value of the test statistic chosen in step 3. This is done by comparing the man of the sample to the mean of the sampling distribution (step 4) relative to the standard deviation of the sampling distribution (step 4).

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Step 7: State it
Make a decision to reject or fail to reject the null hypothesis.

Describe Br. Britt's seven step hypothesis testing procedure for judging whether a difference between a set of means is larger enough to be statistically significant.
Errors (type I/ type II) Can't prove anything because dealing with probabilities. We can be wrong.
 Type I error: say reject the null hypo when the null is true (reality: treatment not effective
 Type II error: say fail to reject the null hypothesis when it is in fact false (reality: treatment is effective)

