Hypothesis Testing
With rare exceptions, an alpha level is never larger than
0.05
common levels of significance / alpha values
0.05, 0.01, 0.001
An alpha level of 0.01 means that _____ or 0.0100 is split between the two tails, so each tail has a proportion of _____.
1%, 0.005 or 0.5%
Logic underlying hypothesis testing: 1) State a _____ about a _____. 2)Use the _____ to predict the characteristics that the _____ should have. 3) Obtain a _____ from the _____. 4) Compare the obtained _____ data with the _____. Check for consistency or ____.
1) hypothesis, population - 2) hypothesis, sample - 3) random sample, population - 4) sample, prediction, discrepancy
Four steps of a hypothesis test
1) state the hypothesis - 2) set the criteria for a decision - 3) collect data and compute sample statistics - 4) make a decision (reject H0 or fail to reject H0)
Because an extreme 5% is split between two tails of the distribution, there is exactly _____ in each tail. In the unit normal table, you look up a proportion of _____ in the tail to find the z-score boundary.
2.5% (0.0250) for both
An alpha of 0.05 will separate the most unlikely _____ of the sample means (the _____ values) from the most likely _____ of the sample means (the _____ values)
5%, extreme, 95%, central
The null hypothesis has the equation of
H0 = number
Example of a Type 1 error (using waitresses wearing red and tips)
It may have been concluded that wearing red increases tips. However, the sample was unrepresentative, and the customers were high tippers regardless of the waitress' clothes. The red had no effect.
The alpha level for a hypothesis test is the probability that the test will lead to a _____.
Type 1 error
Type II error in plain english
a treatment effect really exists, but the hypothesis test failed to detect it
The extremely unlikely values, as defined by the _____ _____, make up what is called the _____ _____. These extreme values in the tails of the distribution define outcomes that are not consistent with the _____ _____.
alpha level, critical region, null hypothesis
The level of significance or _____ _____ is a probability value that is used to define the concept of "_____ _____" in a hypothesis test.
alpha level, very unlikely
A Type 1 error occurs when a researcher obtains an _____ sample
extreme / unrepresentative
We have to see if the sample mean (or whatever) is consistent with the null hypothesis
important
If the sample data's z-score is in the critical region, then you can _________________.
reject the null hypothesis
A researcher typically completes a _____ study and then uses a _____ to evaluate the _____.
research, hypothesis test, results.
The critical region is composed of the extreme _____ values that are very unlikely (based on alpha level) to be obtained if the _____ _____ is true
sample, null hypothesis
A hypothesis test is a _____ that uses _____ to evaluate a hypothesis about a _____.
statistical method, sample data, population
Hypothesis testing is a _____ procedure that allows researchers to use _____ data to draw _____ about the _____ of interest.
statistical, sample, inferences, population
The null hypothesis (H0) states that
the treatment has no effect. The IV has no effect on the DV.
Alternative hypothesis (H1) states that
the treatment, independent variable, has an effect on the dependent variable
Type II error
when a researcher fails to reject the null hypothesis, but the null hypothesis should be rejected (treatment effect exists)
Type 1 Error
when a researcher rejects the null hypothesis when it is actually true. It was concluded that the treatment had an effect, when it actually had no effect.
z-score for sample mean
z = (sample mean - hypothesized population mean) / (standard error between M and μ)
We combine the concepts of _____, _____, and _____ to create the statistical procedure of the hypothesis test.
z-scores, probability, the distribution of sample means
Write the equation: Waitresses wearing red will have a tip that is different than 15.8%.
μ ≠ 15.8 (H1)
