Chapter 08 Introduction to Hypothesis Testing
Which of the following correctly describes the effect that decreasing sample size and decreasing the standard deviation have on the power of a hypothesis test?
A decrease in sample size will decrease the power, but a decrease in standard deviation will increase the power.
Does a hypothesis test allow a researcher to claim that an alternative hypothesis is true?
A hypothesis test does not allow a researcher to claim that an alternative hypothesis is true. A hypothesis test compares the probability of obtaining the sample data if the null hypothesis were true to α , which is the criterion for rejecting the null hypothesis.
If other factors are held constant, then how does the sample size affect the likelihood of rejecting the null hypothesis and the value for Cohen's d?
A larger sample size increases the likelihood of rejecting the null hypothesis but does not change the value of Cohen's d.
Which of the following explains why it is easier to reject the null hypothesis with a one-tailed test than with a two-tailed test with all the same parameters?
Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test
Which of the following is a common limitation of hypothesis testing?
Conclusions are made about the data set rather than about the hypothesis itself. Demonstrating a significant treatment effect does not necessarily indicate a substantial treatment effect.
Assuming a normal distribution, which of the following would call for a one-tailed hypothesis test rather than a two-tailed test?
Determining if driving a red car increases the number of speeding tickets per year
Non Directional Hypothesis
Direction not specified, positive or negative Two tailed Only predicts the existence Appropriate for variables that are not orderable
Which of the following is not a step in a hypothesis test?
If the sample data is not located in the critical region, we accept the null hypothesis
Hypothesis test
Step 1: Determine the null and alternative hypotheses.State the hypotheses and select an alpha level. Step 2: Set the criteria for a decision about the unknown population. Step 3: Collect the data and compute the sample statistic Step 4: Decide whether to reject or fail to reject the null hypothesis.
If the alpha level is changed from α = .05 to α = .01, what happens to boundaries for the critical region?
The boundaries move farther into the tails
What happens to the probability of a Type I error when the alpha level is changed from α = .05 to α = .01?
The probability decreases
Suppose that a treatment effect increases both the mean and the standard deviation of a measurement. Can a hypothesis test with z be conducted?
The z-test cannot be conducted because the test assumes that the treatment affects the mean but not the standard deviation .
What would be the result of setting an alpha level extremely small?
There would be almost no risk of a Type I error. It would be very difficult to reject the null hypothesis.
What is the primary concern when selecting an alpha value?
To minimize Type I errors
For a two-tailed test with α = .05 and σ known
boundaries of the critical region are always ±1.96
Evaluate null hypothesis
by assuming that it is true and testing the reasonableness of this assumption by calculating the probability of getting the results if chance alone is operating.
Criteria for evaluating size of treatment
d=.2 small effect d=.5 medium effect d=.8 large effect
Increasing the number of scores in the sample will
decrease the denominator and so will increase the z-score
changing from one tailed test to a two tailed test
decreases the power of a hypothesis test
Directional Hypothesis
direction is specified One tailed Specifies existence and also relationship Appropriate for variables that are orderable
Type II
error occurs when a researcher fails to reject a null hypothesis that is in fact false.
Type I
error occurs when a researcher rejects a null hypothesis that is actually true.
A type II error is
failing to reject a false null hypothesis This leads to failure to detect a real treatment effect
Increasing the population standard deviation will
increase the denominator and so will decrease the z-score
Increasing the size of the treatment effect will
increase the z-score
An increase in the obtained difference (M - μ)
increases
increase in the sample size
increases
increasing effect size
increases the power of a hypothesis test
increasing the alpha level from .01 to .05
increases the power of a hypothesis test
Effect size
intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used
A larger standard deviation
reduces the likelihood of rejecting the null hypothesis Less extreme values of z result in rejection of the null hypothesis with a one tail test than with a two tail test
A type I error is
rejecting a true null hypothesis. This can result in a false report of a treatment effect that actually does not exist this error is worse
The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error o
rejecting the null hypothesis
The alpha level for a hypothesis test is
small probability value that defines the concept of very unlikely
Which of the following is not an assumption for hypothesis tests with z-scores?
small standard deviations
null hypothesis
states that in the general population there is no change, no difference, or no relationship.
alternative hypothesis
states that there is a change, a difference, or a relationship for the general population.
A switch from using a one-tailed test to a two tailed test
stays the same
decrease in the significance level
stays the same
The critical region is
the area in the tails beyond each z-score
The critical region consists of
the outcomes that are very unlikely to occur as defined by the alpha level if the null hypothesis is true
