Errors
What are the two types of errors and their notations?
Type 1 Error = α (alpha)
Type 2 Error = β (beta)
A random sample REQUIRES that ______
A. every individual has an equal chance of being selected
B. the probabilities cannot change during a series of selections
C. there must be sample with replacement
D. A and C
E. All of the above
E. All of the above
The first step in hypothesis testing is to ________.
check the assumptions
The power of a statistical test is the probability of ____
A. rejecting a true null hypothesis
B. supporting a true null hypothesis
C. rejecting a false null hypothesis
D. supporting a false null hypothesis
C. rejecting a false null hypothesis
What is a Type 1 Error?
You conclude that a significant difference exists when it actually does not
False Positive
Reject Null (difference), Null is correct (no difference) - rejecting a true null hypothesis
The standard deviation of the sampling distribution of sample means is called?
The standard error
What is the null and alternative hypothesis?
Null hypothesis = there is no treatment effect
Alternative Hypothesis = a treatment effect exists
A researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test then the critical region for the test would be ____.
A. entirely in the right hand tail of the distribution
B. entirely in the left hand tail of the distribution
C. divided equally between the two tails
D. Cannot answer without knowing the alpha level
B. entirely in the left-hand tail of the distribution
What is Type 2 Error?
You conclude there is no significant change or relationship when one actually exists.
False Negative
Fail to Reject Null (no diff.), Null is incorrect (diff.)
failing to reject a false null hypothesis
WHen a random sample is selected from a population the samplel mean is not expected to be exactly equal to the population mean. ON average, the size of the difference betweent the sample mean and the population mean is predicted by
A. the standard error
B. the expected value
C. the mean of the population
D. the standard deviation of the population
A. the standard error
A hypothesis test is _______.
A. a descriptive technique that allows researchers to describe a sample
B. a descriptive technique that allows researchers to describe a population
C. an inferential technique that uses information about a population to make predictions about a sample
D. An inferential technique that uses the data from a sample to draw inferences about a population
D. An inferential technique that uses the data from a sample to draw inferences about a population
A. outcomes with a high probability if the null hypothesis is true
B. outcomes with a very lower probability whether or not the null hypothesis is true
C. outcomes with a high probability whether or not the null hypothesis is true
D. outcomes with a very low probability if the null hypothesis is true
D. outcomes with a very low probability if the null hypothesis is true
A research report summarizes the results of the hypothesis test by stating "z = 2.74, p < 0.05)." According to the report ________
A. the null was rejected and probability of a Type 1 error is less than 5%
B. the null was rejected and probability of a Type 2 error is less than 5%
C. the null was not rejected and probability of a Type 1 error is less than 5%
D. the null was not rejected and probability of a Type 2 error is less than 5%
A. the null was rejected and probability of a Type 1 error is less than 5%
According to the central limit theorem as sample size increases the distribution of sample means will be _______?
approximately normal
A two-tailed hypothesis test is being used to evaluate a treatment effect with a = 0.05. If the sample data produced a z score of z = -2.24? then what is the correct decision?
A. reject the null hypothesis and conclude the treatment has no effect
B. Reject the null hypothesis and conclude that the treatment has an effect
C. Fail to reject the null and conclude that the treatment has no effect
D. Fail to reject the null and conclude that the treatment has an effect
B. Reject the null hypothesis and conclude that the treatment has an effect
What is power and when is it most important to calculate it and why?
Power is the probability that a test correctly rejects the null hypothesis when it is false. In other words, it is the chance of detecting a real effect. Power equals 1 − β, where β is the probability of a Type II error.
Power is most important when we fail to reject the null hypothesis. Failing to reject could mean there really is no effect, or it could mean the test was too weak to detect one. If power was low (for example, because the sample was small), we can't be confident the null is true, since we may have made a Type II error. Checking power tells us how much to trust a "no effect" result.
Describe the 4 decision you can make in hypothesis testing.
Rejected Null + True Null = Type 1 Error = false positive = probability (a)
Rejected Null + False Null = Correct Decision = true positive = probability (1-B)
Not Rejected Null + True Null = Correct Decision = true negative = probability (1-a)
Not rejected null + False null = Type 2 error = false negative = probability (B)
The distribution of sample means consists of _______.
A. all the scores contained in the sample
B. all the scores contained in the population
C. All the sammple means that could be obtained (for a specific sample size)
D. the specific sample mean computed from the sample of scores
C. All the sammple means that could be obtained (for a specific sample size)
What is the purpose of checking the normal distribution assumption and the interval/ratio measurement assumption in a hypothesis test?
We check that the population is normal because hypothesis tests assume the sampling distribution shape is normal. If it isn't, the p-values can be wrong, so our conclusion might be wrong too. With a large sample this matters less, because the Central Limit Theorem makes the sampling distribution close to normal anyway.
We check that the data are interval or ratio because the test involves calculating the average. An average only makes sense when the gaps between values are equal, like height or temperature. It doesn't make sense for categories or rankings, nor does it work.
How is the rejection region (critical region) in a hypothesis test determined by the significance level (α) and by the alternative hypothesis? Explain the specific role of each.
Alpha (α) decides the size the rejection region is. A smaller α means a smaller region, so it is harder to reject the null hypothesis.
The alternative hypothesis decides where the rejection region goes. A one-tailed test ("greater than" or "less than") puts the region in one tail. A two-tailed test ("not equal to") splits it between both tails.